Mathematical / Computational / Theoretical physics Books
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Symmetries in Physics: Group Theory Applied to Physical Problems
Book SynopsisSymmetries in Physics presents the fundamental theories of symmetry, together with many examples of applications taken from several different branches of physics. Emphasis is placed on the theory of group representations and on the powerful method of projection operators. The excercises are intended to stimulate readers to apply the techniques demonstrated in the text.Table of Contents1. Introduction.- 2. Elements of the Theory of Finite Groups.- 2.1 Symmetry and Group Concepts: A Basic Example.- 2.2 General Theorems on Group Theory.- 2.3 Conjugacy Classes.- 3. Discrete Symmetry Groups.- 3.1 Point Groups.- 3.1.1 Symmetry Elements.- 3.1.2 Proper Point Groups.- 3.1.3 Improper Point Groups.- 3.2 Colour Groups and Magnetic Groups.- 3.3 Double Groups.- 3.4 Lattices, the Translation Group and Space Group.- 3.4.1 Normal Space Groups.- 3.4.2 Colour and Magnetic Space Groups.- 3.4.3 Double Space Groups.- 3.5 Permutation Groups.- 3.6 Other Finite Groups.- 4. Representations of Finite Groups.- 4.1 Linear Spaces and Operators.- 4.1.1 Linear and Unitary Spaces.- 4.1.2 Linear Operators.- 4.1.3 Special Operators and Eigenvalues.- 4.2 Introduction to the Theory of Representations.- 4.2.1 Operator Representations by Matrices.- 4.2.2 Equivalent Representations and Characters.- 4.2.3 Reducible and Irreducible Representations.- 4.2.4 Orthogonality Theorems.- 4.2.5 Subduction. Reality of Representations.- 4.3 Group Algebra.- 4.3.1 The Regular Representation.- 4.3.2 Projection Operators.- 4.4 Direct Products.- 4.4.1 Representations of Direct Products of Groups.- 4.4.2 The Inner Direct Product of Representations of a Group. Clebsch-Gordan Expansion.- 4.4.3 Simply Reducible Groups.- 5. Irreducible Representations of Special Groups.- 5.1 Point and Double Point Groups.- 5.2 Magnetic Point Groups. Time Reversal.- 5.3 Translation Groups.- 5.4 Permutation Groups.- 5.5 Tensor Representations.- 5.5.1 Tensor Transformations. Irreducible Tensors.- 5.5.2 Induced Representations.- 5.5.3 Irreducible Tensor Spaces.- 5.5.4 Direct Products and Their Reduction.- 6. Tensor Operators and Expectation Values.- 6.1 Tensors and Spinors.- 6.2 The Wigner-Eckart Theorem.- 6.3 Eigenvalue Problems.- 6.4 Perturbation Calculus.- 7. Molecular Spectra.- 7.1 Molecular Vibrations.- 7.1.1 Equation of Motion and Symmetry.- 7.1.2 Determination of Eigenvalues and Eigenvectors.- 7.1.3 Selection Rules.- 7.2 Electron Functions and Spectra.- 7.2.1 Symmetry in Many-Particle Systems.- 7.2.2 Symmetry-Adapted Atomic and Molecular Orbitals.- 7.2.3 The Hückel Method and Ligand Field Theory.- 7.3 Many-Electron Problems.- 7.3.1 Permutation Symmetry.- 7.3.2 Point and Permutation Symmetry. Molecular States.- 7.3.3 The H2 Molecule.- 8. Selection Rules and Matrix Elements.- 8.1 Selection Rules of Tensor Operators.- 8.2 The Jahn-Teller Theorem.- 8.2.1 Spinless States.- 8.2.2 Time Reversal Symmetry.- 8.3 Radiative Transitions.- 8.4 Crystal Field Theory.- 8.4.1 Crystal Field Splitting of Energy Levels.- 8.4.2 Calculation of Splitting.- 8.5 Independent Components of Material Tensors.- 9. Representations of Space Groups.- 9.1 Representations of Normal Space Groups.- 9.1.1 Decompositions into Cosets.- 9.1.2 Induction of the Representations of R.- 9.2 Allowable Irreducible Representations of the Little Group Gk.- 9.2.1 Projective Representations. Representations with a Factor System for $${\mathcal{G}_{{0k}}} = {\mathcal{G}_k}/\mathbb{T}$$.- 9.2.2 Vector Representations of the Groupe $${\mathcal{J}_k} = {\mathcal{G}_k}/{\mathbb{T}_k}$$.- 9.2.3 Representations of Double Space Groups. Spinor Representations.- 9.3 Projection Operators and Basis Functions.- 9.4 Representations of Magnetic Space Groups.- 9.4.1 Corepresentations of Magnetic Space Groups.- 9.4.2 Time Reversal Symmetry in MII Groups.- 10. Excitation Spectra and Selection Rules in Crystals.- 10.1 Spectra — Some General Statements.- 10.1.1 Bands and Branches.- 10.1.2 Compatibility Relations.- 10.2 Lattice Vibrations.- 10.2.1 Equation of Motion and Symmetry Properties.- 10.2.2 Vibrations of the Diamond Lattice.- 10.3 Electron Energy Bands.- 10.3.1 Symmetrization of Plane Waves.- 10.3.2 Energy Bands and Atomic Levels.- 10.4 Selection Rules for Interactions in Crystals.- 10.4.1 Determination of Reduction Coefficients.- 10.4.2 General Selection Rules.- 10.4.3 Electron-Phonon Interaction.- 10.4.4 Electron-Photon Interaction: Optical Transitions.- 10.4.5 Phonon-Photon Interaction.- 11. Lie Groups and Lie Algebras.- 11.1 General Foundations.- 11.1.1 Infinitesimal Generators and Defining Relations.- 11.1.2 Algebra and Parameter Space.- 11.1.3 Casimir Operators.- 11.2 Unitary Representations of Lie Groups.- 11.3 Clebsch-Gordan Coefficients and the Wigner-Eckart.- Theorem.- 11.4 The Cartan-Weyl Basis for Semisimple Lie Algebras.- 11.4.1 The Lie Group LU (n, ?) and the Lie Algebra An-1..- 11.4.2 The Cartan-Weyl Basis.- 12. Representations by Young Diagrams. The Method of Irreducible Tensors.- 13. Applications of the Theory of Continuous Groups.- 13.1 Elementary Particle Spectra.- 13.1.1 General Remarks.- 13.1.2 Hadronic States.- 13.1.3 Colour States of Quarks.- 13.1.4 A Possible LU (4) Classification.- 13.2 Atomic Spectra.- 13.2.1 Russell-Saunders (LS) Coupling.- 13.2.2 jj Coupling.- 13.3 Nuclear Spectra.- 13.3.1 jj-JI Coupling.- 13.3.2 LSI Coupling.- 13.4 Dynamical Symmetries of Classical Systems.- 14. Internal Symmetries and Gauge Theories.- 14.1 Internal Symmetries of Fields.- 14.2 Gauge Transformations of the First Kind.- 14.2.1 U (1) Gauge Transformations.- 14.2.2 LU (n) Gauge Transformations.- 14.3 Gauge Transformations of the Second Kind.- 14.3.1 U (1) Gauge Transformations of the Second Kind.- 14.3.2 LU (n) Gauge Transformations of the Second Kind.- 14.3.3 A Differential Geometric Discussion of the Yang-Mills Fields.- 14.4 Gauge Theories with Spontaneously Broken Symmetry.- 14.4.1 General Remarks.- 14.4.2 Spontaneous Breaking of a Gauge Symmetry of the First Kind: Goldstone Model.- 14.4.3 Spontaneous Breaking of an Abelian Gauge Symmetry of the Second Kind: Higgs-Kibble Model.- 14.5 Non-Abelian Gauge Theories and Symmetry Breaking.- 14.5.1 The Glashow-Salam-Weinberg Model of the Electro-Weak Interaction.- 14.5.2 Symmetry Breaking in the Glashow-Salam-Weinberg Model.- 14.5.3 Grand Unified Theories: General Remarks.- 14.5.4 LU (5) Group and Georgi-Glashow Model.- 14.5.5 Some Consequences of LU (5) Theory.- Appendices.- A. Character Tables.- B. Representations of Generators.- C. Standard Young-Yamanouchi Representations of the Permutation Groups P3 - P5.- D. Continuous Groups.- E. Stars of k and Symmetry of Special k-Vectors.- F. Noether’s Theorem.- G. Space-Time Symmetry.- G.1 Canonical Transformations and Algebra.- G.2 The Galilei Group and Classical Mechanics.- G.3 Lorentz and Poincaré Groups.- G.4 The Physical Quantities.- H. Goldstone’s Theorem.- I. Remarks on 5-fold Symmetry.- J. Supersymmetry.- K. List of Symbols and Abbreviations.- References.- Additional Reading.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Local Quantum Physics: Fields, Particles,
Book SynopsisThe new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics". It was a tempting challenge to try to sharpen the points at issue in the long lasting debate on the Copenhagen Spirit, to assess the significance of various arguments from our present vantage point, seventy years after the advent of quantum theory, where, after ali, some problems appear in a different light. It includes a section on the assumptions leading to the specific mathematical formalism of quantum theory and a section entitled "The evolutionary picture" describing my personal conclusions. Alto gether the discussion suggests that the conventional language is too narrow and that neither the mathematical nor the conceptual structure are built for eter nity. Future theories will demand radical changes though not in the direction of a return to determinism. Essential lessons taught by Bohr will persist. This chapter is essentially self-contained. Some new material has been added in the last chapter. It concerns the char acterization of specific theories within the general frame and recent progress in quantum field theory on curved space-time manifolds. A few pages on renor malization have been added in Chapter II and some effort has been invested in the search for mistakes and unclear passages in the first edition. The central objective of the book, expressed in the title "Local Quantum Physics", is the synthesis between special relativity and quantum theory to gether with a few other principles of general nature.Trade Review"Indeed, both the expert in the field and the novice will enjoy Haags insightful exposition... This (superb) book is bound to occupy a place on a par with other classics in the mathematical physics literature." Physics Today "...enjoyable reading to anybody interested in the development of fundamental physical theories." Zentralblatt f. MathematikTable of ContentsI. Background.- 1. Quantum Mechanics.- Basic concepts, mathematical structure, physical interpretation..- 2. The Principle of Locality in Classical Physics and the Relativity Theories.- Faraday’s vision. Fields..- 2.1 Special relativity. Poincaré group. Lorentz group. Spinors. Conformal group..- 2.2 Maxwell theory..- 2.3 General relativity..- 3. Poincaré Invariant Quantum Theory.- 3.1 Geometric symmetries in quantum physics. Projective representations and the covering group..- 3.2 Wigner’s analysis of irreducible, unitary representations of the Poincare group. 3.3 Single particle states. Spin..- 3.4 Many particle states: Bose-Fermi alternative, Fock space, creation operators. Separation of CM-motion..- 4. Action Principle.- Lagrangean. Double rôle of physical quantities. Peierls’ direct definition of Poisson brackets. Relation between local conservation laws and symmetries..- 5. Basic Quantum Field Theory.- 5.1 Canonical quantization..- 5.2 Fields and particles..- 5.3 Free fields..- 5.4 The Maxwell-Dirac system. Gauge invariance..- 5.5 Processes..- II. General Quantum Field Theory.- 1. Mathematical Considerations and General Postulates.- 1.1 The representation problem..- 1.2 Wightman axioms..- 2. Hierarchies of Functions.- 2.1 Wightman functions, reconstruction theorem, analyticity in x-space..- 2.2 Truncated functions, clustering. Generating functionals and linked cluster theorem..- 2.3 Time ordered functions..- 2.4 Covariant perturbation theory, Feynman diagrams. Renormalization..- 2.5 Vertex functions and structure analysis..- 2.6 Retarded functions and analyticity in p-space..- 2.7 Schwinger functions and Osterwalder-Schrader theorem..- 3. Physical Interpretation in Terms of Particles.- 3.1 The particle picture: Asymptotic particle configurations and collision theory..- 3.2 Asymptotic fields. S-matrix..- 3.3 LSZ-formalism..- 4. General Collision Theory.- 4.1 Polynomial algebras of fields. Almost local operators..- 4.2 Construction of asymptotic particle states..- 4.3. Coincidence arrangements of detectors..- 4.4 Generalized LSZ-formalism..- 5. Some Consequences of the Postulates.- 5.1 CPT-operator. Spin-statistics theorem. CPT-theorem..- 5.2 Analyticity of the S-matrix..- 5.3 Reeh-Schlieder theorem..- 5.4 Additivity of the energy-momentum-spectrum..- 5.5 Borchers classes..- III. Algebras of Local Observables and Fields.- 1. Review of the Perspective.- Characterization of the theory by a net of local algebras. Bounded operators. Unobservable fields, superselection rules and the net of abstract algebras of observables. Transcription of the basic postulates..- 2. Von Neumann Algebras. C*-Algebras. W*-Algebras.- 2.1 Algebras of bounded operators. Concrete C*-algebras and von Neumann algebras. Isomorphisms. Reduction. Factors. Classification of factors..- 2.2 Abstract algebras and their representations. Abstract C*-algebras. Relation between the C*-norm and the spectrum. Positive linear forms and states. The GNS-construction. Folia of states. Intertwiners. Primary states and cluster property. Purification. W*-algebras..- 3. The Net of Algebras of Local Observables.- 3.1 Smoothness and integration. Local definiteness and local normality..- 3.2 Symmetries and symmetry breaking. Vacuum states. The spectral ideals..- 3.3 Summary of the structure..- 4. The Vacuum Sector.- 4.1 The orthocomplemented lattice of causally complete regions..- 4.2 The net of von Neumann algebras in the vacuum representation..- IV. Charges, Global Gauge Groups and Exchange Symmetry.- 1. Charge Superselection Sectors.- “Strange statistics”. Charges. Selection criteria for relevant sectors. The program and survey of results..- 2. The DHR-Analysis.- 2.1 Localized morphisms..- 2.2 Intertwiners and exchange symmetry (“Statistics”)..- 2.3 Charge conjugation, statistics parameter..- 2.4 Covariant sectors and energy-momentum spectrum..- 2.5 Fields and collision theory..- 3. The Buchholz-Fredenhagen-Analysis.- 3.1 Localized 1-particle states..- 3.2 BF-topological charges..- 3.3 Composition of sectors and exchange symmetry..- 3.4 Charge conjugation and the absence of “infinite statistics”..- 4. Global Gauge Group and Charge Carrying Fields.- Implementation of endomorphisms. Charges with d = 1. Endomorphisms and non Abelian gauge group. DR categories and the embedding theorem..- 5. Low Dimensional Space-Time and Braid Group Statistics.- Statistics operator and braid group representations. The 2+1-dimensional case with BF-charges. Statistics parameter and Jones index..- V. Thermal States and Modular Automorphisms.- 1. Gibbs Ensembles, Thermodynamic Limit, KMS-Condition.- 1.1 Introduction..- 1.2 Equivalence of KMS-condition to Gibbs ensembles for finite volume..- 1.3 The arguments for Gibbs ensembles..- 1.4 The representation induced by a KMS-state..- 1.5 Phases, symmetry breaking and the decomposition of KMS-states..- 1.6 Variational principles and autocorrelation inequalities..- 2. Modular Automorphisms and Modular Conjugation.- 2.1 The Tomita-Takesaki theorem..- 2.2 Vector representatives of states. Convex cones in H..- 2.3 Relative modular operators and Radon-Nikodym derivatives..- 2.4 Classification of factors..- 3. Direct Characterization of Equilibrium States.- 3.1 Introduction..- 3.2 Stability..- 3.3 Passivity..- 3.4 Chemical potential..- 4. Modular Automorphisms of Local Algebras.- 4.1 The Bisognano-Wichmann theorem..- 4.2 Conformal invariance and the theorem of Hislop and Longo..- 5. Phase Space, Nuclearity, Split Property, Local Equilibrium.- 5.1 Introduction..- 5.2 Nuclearity and split property..- 5.3 Open subsystems..- 5.4 Modular nuclearity..- 6. The Universal Type of Local Algebras.- VI. Particles. Completeness of the Particle Picture.- 1. Detectors, Coincidence Arrangements, Cross Sections.- 1.1 Generalities..- 1.2 Asymptotic particle configurations. Buchholz’s strategy..- 2. The Particle Content.- 2.1 Particles and infraparticles..- 2.2 Single particle weights and their decomposition..- 2.3 Remarks on the particle picture and its completeness..- 3. The Physical State Space of Quantum Electrodynamics.- VII. Principles and Lessons of Quantum Physics. A Review of Interpretations, Mathematical Formalism and Perspectives.- 1. The Copenhagen Spirit. Criticisms, Elaborations.- Niels Bohr’s epistemological considerations. Realism. Physical systems and the division problem. Persistent non-classical correlations. Collective coordinates, decoherence and the classical approximation. Measurements. Correspondence and quantization. Time reflection asymmetry of statistical conclusions..- 2. The Mathematical Formalism.- Operational assumptions. “Quantum Logic”. Convex cones..- 3. The Evolutionary Picture.- Events, causal links and their attributes. Irreversibility. The EPR-effect. Ensembles vs. individuals. Decisions. Comparison with standard procedure..- VIII. Retrospective and Outlook.- 1. Algebraic Approach vs. Euclidean Quantum Field Theory.- 2. Supersymmetry.- 3. The Challenge from General Relativity.- 3.1 Introduction..- 3.2 Quantum field theory in curved space-time..- 3.3 Hawking temperature and Hawking radiation..- 3.4 A few remarks on quantum gravity..- Author Index and References.
£66.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Operator Algebras and Quantum Statistical Mechanics: Equilibrium States. Models in Quantum Statistical Mechanics
Book SynopsisFor almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions. Table of ContentsVolume 2.- States in Quantum Statistical Mechanics.- 5.1. Introduction.- 5.2. Continuous Quantum Systems. I.- 5.3. KMS-States.- 5.4. Stability and Equilibrium.- Models of Quantum Statistical Mechanics.- 6.1. Introduction.- 6.2 Quantum Spin Systems.- 6.3. Continuous Quantum Systems. II.- 6.4. Conclusion.- References.- Books and Monographs.- Articles.- List of Symbols.
£142.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Lectures on Nonlinear Hyperbolic Differential
Book SynopsisIn this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.Table of ContentsPreface.- Contents.- Chap. I: Ordinary differential equations.- Chap. II: Scalar first order equations with one space variable.- Chap. III: Scalar first order equations with several variables.- Chap. IV: First order systems of conservation laws with one space.- Chap. V: Compensated compactness.- Chap. VI: Nonlinear perturbations of the wave equation.- Chap. VII: Nonlinear perturbations of the Klein-Gordon equation.- Chap. VIII: Microlocal analysis.- Chap. IX: Pseudo-differential operators of type 1,1.- Chap. X: Paradifferential calculus.- Chap. XI: Propagation of singularities.- Appendix on pseudo-Riemannian geometry.- References.- Index of notations.- Index.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Foundations of the Classical Theory of Partial Differential Equations
Book SynopsisFrom the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery...." The Mathematical Gazette, 1993Trade ReviewFrom the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... According to the authors ... the work was written for the nonspecialists and physicists but in my opinion almost every specialist will find something new for herself/himself in the text. ..." Acta Scientiarum Mathematicarum, 1993 "... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume." Monatshefte für Mathematik, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery...." The Mathematical Gazette, 1993Table of Contents1. Basic Concepts.- 1. Basic Definitions and Examples.- 1.1. The Definition of a Linear Partial Differential Equation.- 1.2. The Role of Partial Differential Equations in the Mathematical Modeling of Physical Processes.- 1.3. Derivation of the Equation for the Longitudinal Elastic Vibrations of a Rod.- 1.4. Derivation of the Equation of Heat Conduction.- 1.5. The Limits of Applicability of Mathematical Models.- 1.6. Initial and Boundary Conditions.- 1.7. Examples of Linear Partial Differential Equations.- 1.8. The Concept of Well-Posedness of a Boundary-value Problem. The Cauchy Problem.- 2. The Cauchy-Kovalevskaya Theorem and Its Generalizations.- 2.1. The Cauchy-Kovalevskaya Theorem.- 2.2. An Example of Nonexistence of an Analytic Solution.- 2.3. Some Generalizations of the Cauchy-Kovalevskaya Theorem. Characteristics.- 2.4. Ovsyannikov’s Theorem.- 2.5. Holmgren’s Theorem.- 3. Classification of Linear Differential Equations. Reduction to Canonical Form and Characteristics.- 3.1. Classification of Second-Order Equations and Their Reduction to Canonical Form at a Point.- 3.2. Characteristics of Second-Order Equations and Reduction to Canonical Form of Second-Order Equations with Two Independent Variables.- 3.3. Ellipticity, Hyperbolicity, and Parabolicity for General Linear Differential Equations and Systems.- 3.4. Characteristics as Solutions of the Hamilton-Jacobi Equation.- 2. The Classical Theory.- 1. Distributions and Equations with Constant Coefficients.- 1.1. The Concept of a Distribution.- 1.2. The Spaces of Test Functions and Distributions.- 1.3. The Topology in the Space of Distributions.- 1.4. The Support of a Distribution. The General Form of Distributions.- 1.5. Differentiation of Distributions.- 1.6. Multiplication of a Distribution by a Smooth Function. Linear Differential Operators in Spaces of Distributions.- 1.7. Change of Variables and Homogeneous Distributions.- 1.8. The Direct or Tensor Product of Distributions.- 1.9. The Convolution of Distributions.- 1.10. The Fourier Transform of Tempered Distributions.- 1.11. The Schwartz Kernel of a Linear Operator.- 1.12. Fundamental Solutions for Operators with Constant Coefficients.- 1.13. A Fundamental Solution for the Cauchy Problem.- 1.14. Fundamental Solutions and Solutions of Inhomogeneous Equations.- 1.15. Duhamel’s Principle for Equations with Constant Coefficients.- 1.16. The Fundamental Solution and the Behavior of Solutions at Infinity.- 1.17. Local Properties of Solutions of Homogeneous Equations with Constant Coefficients. Hypoellipticity and Ellipticity.- 1.18. Liouville’s Theorem for Equations with Constant Coefficients.- 1.19. Isolated Singularities of Solutions of Hypoelliptic Equations.- 2. Elliptic Equations and Boundary-Value Problems.- 2.1. The Definition of Ellipticity. The Laplace and Poisson Equations.- 2.2. A Fundamental Solution for the Laplacian Operator. Green’s Formula.- 2.3. Mean-Value Theorems for Harmonic Functions.- 2.4. The Maximum Principle for Harmonic Functions and the Normal Derivative Lemma.- 2.5. Uniqueness of the Classical Solutions of the Dirichlet and Neumann Problems for Laplace’s Equation.- 2.6. Internal A Priori Estimates for Harmonic Functions. Harnack’s Theorem.- 2.7. The Green’s Function of the Dirichlet Problem for Laplace’s Equation.- 2.8. The Green’s Function and the Solution of the Dirichlet Problem for a Ball and a Half-Space. The Reflection Principle.- 2.9. Harnack’s Inequality and Liouville’s Theorem.- 2.10. The Removable Singularities Theorem.- 2.11. The Kelvin Transform and the Statement of Exterior Boundary-Value Problems for Laplace’s Equation.- 2.12. Potentials.- 2.13. Application of Potentials to the Solution of Boundary-Value Problems.- 2.14. Boundary-Value Problems for Poisson’s Equation in Hölder Spaces. Schauder Estimates.- 2.15. Capacity.- 2.16. The Dirichlet Problem in the Case of Arbitrary Regions (The Method of Balayage). Regularity of a Boundary Point. The Wiener Regularity Criterion.- 2.17. General Second-Order Elliptic Equations. Eigenvalues and Eigenfunctions of Elliptic Operators.- 2.18. Higher-Order Elliptic Equations and General Elliptic Boundary-Value Problems. The Shapiro-Lopatinskij Condition.- 2.19. The Index of an Elliptic Boundary-Value Problem.- 2.20. Ellipticity with a Parameter and Unique Solvability of Elliptic Boundary-Value Problems.- 3. Sobolev Spaces and Generalized Solutions of Boundary-Value Problems.- 3.1. The Fundamental Spaces.- 3.2. Imbedding and Trace Theorems.- 3.3. Generalized Solutions of Elliptic Boundary-Value Problems and Eigenvalue Problems.- 3.4. Generalized Solutions of Parabolic Boundary-Value Problems.- 3.5. Generalized Solutions of Hyperbolic Boundary-Value Problems.- 4. Hyperbolic Equations.- 4.1. Definitions and Examples.- 4.2. Hyperbolicity and Well-Posedness of the Cauchy Problem.- 4.3. Energy Estimates.- 4.4. The Speed of Propagation of Disturbances.- 4.5. Solution of the Cauchy Problem for the Wave Equation.- 4.6. Huyghens’ Principle.- 4.7. The Plane Wave Method.- 4.8. The Solution of the Cauchy Problem in the Plane.- 4.9. Lacunae.- 4.10. The Cauchy Problem for a Strictly Hyperbolic System with Rapidly Oscillating Initial Data.- 4.11. Discontinuous Solutions of Hyperbolic Equations.- 4.12. Symmetric Hyperbolic Operators.- 4.13. The Mixed Boundary-Value Problem.- 4.14. The Method of Separation of Variables.- 5. Parabolic Equations.- 5.1. Definitions and Examples.- 5.2. The Maximum Principle and Its Consequences.- 5.3. Integral Estimates.- 5.4. Estimates in Hölder Spaces.- 5.5. The Regularity of Solutions of a Second-Order Parabolic Equation.- 5.6. Poisson’s Formula.- 5.7. A Fundamental Solution of the Cauchy Problem for a Second-Order Equation with Variable Coefficients.- 5.8. Shilov-Parabolic Systems.- 5.9. Systems with Variable Coefficients.- 5.10. The Mixed Boundary-Value Problem.- 5.11. Stabilization of the Solutions of the Mixed Boundary-Value Problem and the Cauchy Problem.- 6. General Evolution Equations.- 6.1. The Cauchy Problem. The Hadamard and Petrovskij Conditions.- 6.2. Application of the Laplace Transform.- 6.3. Application of the Theory of Semigroups.- 6.4. Some Examples.- 7. Exterior Boundary-Value Problems and Scattering Theory.- 7.1. Radiation Conditions.- 7.2. The Principle of Limiting Absorption and Limiting Amplitude.- 7.3. Radiation Conditions and the Principle of Limiting Absorption for Higher-Order Equations and Systems.- 7.4. Decay of the Local Energy.- 7.5. Scattering of Plane Waves.- 7.6. Spectral Analysis.- 7.7. The Scattering Operator and the Scattering Matrix.- 8. Spectral Theory of One-Dimensional Differential Operators.- 8.1. Outline of the Method of Separation of Variables.- 8.2. Regular Self-Adjoint Problems.- 8.3. Periodic and Antiperiodic Boundary Conditions.- 8.4. Asymptotics of the Eigenvalues and Eigenfunctions in the Regular Case.- 8.5. The Schrödinger Operator on a Half-Line.- 8.6. Essential Self-Adjointness and Self-Adjoint Extensions. The Weyl Circle and the Weyl Point.- 8.7. The Case of an Increasing Potential.- 8.8. The Case of a Rapidly Decaying Potential.- 8.9. The Schrödinger Operator on the Entire Line.- 8.10. The Hill Operator.- 9. Special Functions.- 9.1. Spherical Functions.- 9.2. The Legendre Polynomials.- 9.3. Cylindrical Functions.- 9.4. Properties of the Cylindrical Functions.- 9.5. Airy’s Equation.- 9.6. Some Other Classes of Functions.- References.- Author Index.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Scaling Limits of Interacting Particle Systems
Book SynopsisThis book has been long awaited in the "interacting particle systems" community. Begun by Claude Kipnis before his untimely death, it was completed by Claudio Landim, his most brilliant student and collaborator. It presents the techniques used in the proof of the hydrodynamic behavior of interacting particle systems.Trade Review"Das Buch ist nach Meinung des Rezensenten eine gelungene Einführung in ein interessantes Gebiet der modernen Stochastik und mathematischen Physik und stellt einen fest umrissenen Gegenstand umfassend dar, vor allem den analytisch-methodischen Aspekt. ... Die Beweise sind übersichtlich und gut gegliedert, was das Nachvollziehen der Argumente sehr erleichtert; die didaktische Leistung der Autoren in diesem Punkt ist beeindruckend. Ein sorgfältig zusammengestelltes Literaturverzeichnis von etwa 400 Titeln schließt das Buch ab. Ingesamt ein sehr gut geschriebener und nützlicher Band."DMV Jahresbericht, 103. Band, Heft 3, November 2001Table of Contents1. An Introductory Example: Independent Random Walks.- 2. Some Interacting Particle Systems.- 3. Weak Formulations of Local Equilibrium.- 4. Hydrodynamic Equation of Symmetric Simple Exclusion Processes.- 5. An Example of Reversible Gradient System: Symmetric Zero Range Processes.- 6. The Relative Entropy Method.- 7. Hydrodynamic Limit of Reversible Nongradient Systems.- 8. Hydrodynamic Limit of Asymmetric Attractive Processes.- 9. Conservation of Local Equilibrium for Attractive Systems.- 10. Large Deviations from the Hydrodynamic Limit.- 11. Equilibrium Fluctuations of Reversible Dynamics.- Appendices.- 1. Markov Chains on a Countable Space.- 1.1 Discrete Time Markov Chains.- 1.2 Continuous Time Markov Chains.- 1.3 Kolmogorov’s Equations, Generators.- 1.4 Invariant Measures, Reversibility and Adjoint Processes.- 1.5 Some Martingales in the Context of Markov Processes.- 1.6 Estimates on the Variance of Additive Functionals of Markov Processes.- 1.7 The Feynman-Kac Formula.- 1.8 Relative Entropy.- 1.9 Entropy and Markov Processes.- 1.10 Dirichlet Form.- 1.11 A Maximal Inequality for Reversible Markov Processes.- 2. The Equivalence of Ensembles, Large Deviation Tools and Weak Solutions of Quasi-Linear Differential Equations.- 2.1 Local Central Limit Theorem and Equivalence of Ensembles.- 2.2 On the Local Central Limit Theorem.- 2.3 Remarks on Large Deviations.- 2.4 Weak Solutions of Nonlinear Parabolic Equations.- 2.5 Entropy Solutions of Quasi-Linear Hyperbolic Equations.- 3. Nongradient Tools: Spectral Gap and Closed Forms.- 3.1 On the Spectrum of Reversible Markov Processes.- 3.2 Spectral Gap for Generalized Exclusion Processes.- 3.4 Closed and Exact Forms.- 3.5 Comments and References.- References.
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Field Theory in Condensed Matter Physics
Book SynopsisThis is an approachable introduction to the important topics and recent developments in the field of condensed matter physics. First, the general language of quantum field theory is developed in a way appropriate for dealing with systems having a large number of degrees of freedom. This paves the way for a description of the basic processes in such systems. Applications include various aspects of superfluidity and superconductivity, as well as a detailed description of the fractional quantum Hall liquid.Table of ContentsQuantum Mechanics and Fundamentals of Quantum Field Theory.- Path Integral Quantization.- Broken Symmetry and Phase Transition.- Some Applications - Warming Ups.- Superconductivity.- Quantum Hall Liquids and Chern--Simons Gauge Field.- Appendix.
£132.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Hamiltonian Methods in the Theory of Solitons
Book SynopsisThe main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.Trade Review Table of ContentsThe Nonlinear Schrödinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples and Their General Properties.- Fundamental Continuous Models.- Fundamental Models on the Lattice.- Lie-Algebraic Approach to the Classification and Analysis of Integrable Models.- Conclusion.- Conclusion.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Vector Calculus
Book SynopsisVector calculus is the fundamental language of mathematical physics. It pro vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.Trade ReviewP.C. Matthews Vector Calculus "Written for undergraduate students in mathematics, the book covers the material in a comprehensive but concise manner, combining mathematical rigor with physical insight. There are many diagrams to illustrate the physical meaning of the mathematical concepts, which essential for a full understanding of the subject." — ZENTRALBLATT MATH Table of Contents1. Vector Algebra.- 1.1 Vectors and scalars.- 1.1.1 Definition of a vector and a scalar.- 1.1.2 Addition of vectors.- 1.1.3 Components of a vector.- 1.2 Dot product.- 1.2.1 Applications of the dot product.- 1.3 Cross product.- 1.3.1 Applications of the cross product.- 1.4 Scalar triple product.- 1.5 Vector triple product.- 1.6 Scalar fields and vector fields.- 2. Line, Surface and Volume Integrals.- 2.1 Applications and methods of integration.- 2.1.1 Examples of the use of integration.- 2.1.2 Integration by substitution.- 2.1.3 Integration by parts.- 2.2 Line integrals.- 2.2.1 Introductory example: work done against a force.- 2.2.2 Evaluation of line integrals.- 2.2.3 Conservative vector fields.- 2.2.4 Other forms of line integrals.- 2.3 Surface integrals.- 2.3.1 Introductory example: flow through a pipe.- 2.3.2 Evaluation of surface integrals.- 2.3.3 Other forms of surface integrals.- 2.4 Volume integrals.- 2.4.1 Introductory example: mass of an object with variable density.- 2.4.2 Evaluation of volume integrals.- 3. Gradient, Divergence and Curl.- 3.1 Partial differentiation and Taylor series.- 3.1.1 Partial differentiation.- 3.1.2 Taylor series in more than one variable.- 3.2 Gradient of a scalar field.- 3.2.1 Gradients, conservative fields and potentials.- 3.2.2 Physical applications of the gradient.- 3.3 Divergence of a vector field.- 3.3.1 Physical interpretation of divergence.- 3.3.2 Laplacian of a scalar field.- 3.4 Curl of a vector field.- 3.4.1 Physical interpretation of curl.- 3.4.2 Relation between curl and rotation.- 3.4.3 Curl and conservative vector fields.- 4. Suffix Notation and its Applications.- 4.1 Introduction to suffix notation.- 4.2 The Kronecker delta ?ij.- 4.3 The alternating tensor ?ijk.- 4.4 Relation between ?ijk and ?ij.- 4.5 Grad, div and curl in suffix notation.- 4.6 Combinations of grad, div and curl.- 4.7 Grad, div and curl applied to products of functions.- 5. Integral Theorems.- 5.1 Divergence theorem.- 5.1.1 Conservation of mass for a fluid.- 5.1.2 Applications of the divergence theorem.- 5.1.3 Related theorems linking surface and volume integrals.- 5.2 Stokes’s theorem.- 5.2.1 Applications of Stokes’s theorem.- 5.2.2 Related theorems linking line and surface integrals.- 6. Curvilinear Coordinates.- 6.1 Orthogonal curvilinear coordinates.- 6.2 Grad, div and curl in orthogonal curvilinear coordinate systems.- 6.2.1 Gradient.- 6.2.2 Divergence.- 6.2.3 Curl.- 6.3 Cylindrical polar coordinates.- 6.4 Spherical polar coordinates.- 7. Cartesian Tensors.- 7.1 Coordinate transformations.- 7.2 Vectors and scalars.- 7.3 Tensors.- 7.3.1 The quotient rule.- 7.3.2 Symmetric and anti-symmetric tensors.- 7.3.3 Isotropic tensors.- 7.4 Physical examples of tensors.- 7.4.1 Ohm’s law.- 7.4.2 The inertia tensor.- 8. Applications of Vector Calculus.- 8.1 Heat transfer.- 8.2 Electromagnetism.- 8.2.1 Electrostatics.- 8.2.2 Electromagnetic waves in a vacuum.- 8.3 Continuum mechanics and the stress tensor.- 8.4 Solid mechanics.- 8.5 Fluid mechanics.- 8.5.1 Equation of motion for a fluid.- 8.5.2 The vorticity equation.- 8.5.3 Bernoulli’s equation.- Solutions.
£29.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Wissenschaftliches Rechnen
Book SynopsisDas Ziel des nun auch in deutscher Übersetzung erhältlichen Buches ist es, angewandte Mathematik und Ingenieurmathematik so darzustellen, wie sie heutzutage Anwendung findet. Das Buch basiert auf dem Kurs „Wissenschaftliches Rechnen" des Massachusetts Institute of Technology und versucht, Konzepte und Algorithmen zusammenzuführen. Beginnend mit der angewandten linearen Algebra entwickeln die Autoren die Methoden der finiten Differenzen und finiten Elemente – stets in Verbindung mit Anwendungen in zahlreichen Wissensgebieten.Trade Review“... Der in jeder Hinsicht hervorragende Text von Strang wird für lange Zeit eine Standardreferenz in der Literatur zur Ausbildung im wissenschaftlichen Rechnen sein. Es gibt viele gute Gründe, ihn zu besitzen ...” (H.R. Schneebeli, in: Elemente der Mathematik, jg. 67, S. 200 f. 2012)“... Das Buch enthält zahlreiche Aufgaben in unterschiedlichen Schwierigkeitsgraden und drei Anhänge und ist, wenn man es nicht als Begleitbuch zu einer Vorlesung gebraucht, hervorragend zum Stöbern geeignet. ... ist das Buch äußerst empfehlenswert nicht nur für Ingenieure. Teile des Buches sind sicher auch schon für begabte und interessierte Schülerinnen und Schüler geeignet und von Pseudoanwendungen in Schulbüchern genervte Lehrkräfte an unseren Gymnasien können hier realistische Anwendungen finden, die man mit Mathematik bearbeiten kann.“ (in: Mathematische Semesterberichte, 2012, Issue 1)“... in diesem umfangreichen, ursprünglich in englisch erschienenem Werk mit mathematischer Exaktheit und anwendungsorientierter Zielrichtung ... Angesprochen sind vorwiegend Studierende der Mathematik und der Ingenieurwissenschaften. ... Der kurze Anhang ist allenfalls geeignet, Erinnerungslücken zu schließen.“ (Wolfgang Grölz, in: ekz-Informationsdienst, 2010, Vol. 2010/34)Table of ContentsAngewandte lineare Algebra.- Ein Grundmuster der angewandten Mathematik.- Randwertprobleme.- Fourier-Reihen und Fourier-Integrale.- Analytische Funktionen.- Anfangswertprobleme.- Große Systeme.- Optimierung und Minimumprinzip.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Number Theory in Science and Communication: With
Book Synopsis"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudo primes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography. From reviews of earlier editions – "I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvelous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American) "A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin GardnerTrade ReviewFrom the reviews of the fifth edition:“Number theory has been a very active field in the last twenty-seven years, and Schroeder’s text has a palimpsest quality, with later mathematical advances layered on earlier ones. … Number Theory in Science and Communication is rewarding to browse, or as a jumping-off point for further research … . It would be a good source of student projects in an undergraduate discrete mathematics or number theory course.” (Ursula Whitcher, The Mathematical Association of America, March, 2011)Table of ContentsA Few Fundamentals.- The Natural Numbers.- Primes.- The Prime Distribution.- Some Simple Applications.- Fractions: Continued, Egyptian and Farey.- Congruences and the Like.- Linear Congruences.- Diophantine Equations.- The Theorems of Fermat Wilson and Euler.- Permutations Cycles and Derangements.- Cryptography and Divisors.- Euler Trap Doors and Public-Key Encryption.- The Divisor Functions.- The Prime Divisor Functions.- Certified Signatures.- Primitive Roots.- Knapsack Encryption.- Residues and Diffraction.- Quadratic Residues.- Chinese and Other Fast Algorithms.- The Chinese Remainder Theorem and Simultaneous Congruences.- Fast Transformation and Kronecker Products.- Quadratic Congruences.- Pseudoprimes, Möbius Transform, and Partitions.- Pseudoprimes Poker and Remote Coin Tossing.- The Möbius Function and the Möbius Transform.- Generating Functions and Partitions.- From Error Correcting Codes to Covering Sets.- Cyclotomy and Polynomials.- Cyclotomic Polynomials.- Linear Systems and Polynomials.- Polynomial Theory.- Galois Fields and More Applications.- Galois Fields.- Spectral Properties of Galois Sequences.- Random Number Generators.- Waveforms and Radiation Patterns.- Number Theory Randomness and “Art”.- Self-Similarity, Fractals and Art.- Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter.
£56.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Group Theory: Application to the Physics of Condensed Matter
Book SynopsisThis concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.Trade ReviewFrom the reviews:"It was developed for a graduate course taught mostly by Millie Dresselhaus at MIT for more than 30 years, with many revisions of lecture notes. Very much a graduate text or specialist monograph, the book covers a wealth of applications across solid-state physics. … The book can be warmly recommended to students and researchers in solid-state physics, either to serve as a text for an advanced lecture course or for individual study … ." (Volker Heine, Physics Today, November, 2008)"This textbook is based on the authors’ pedagogical experience during their 30 years at MIT. … the book develops all of the relevant mathematics (linear algebra) and the necessary physics (quantum mechanics), it is eminently suitable to a wide audience in physics, chemistry and materials science." (Barry R. Masters, Optics and Photonics News, July/August, 2009)“This is an excellent text … . originates from lectures by Charles Kittel and J. H. van Vleck in the 1950s and much of the material was presented in courses by the authors over the last three decades. The material is meant for Electrical Engineering and Physics students at the graduate level … . has exercises at the end of each chapter and an extensive set of appendices. The exposition is clear and detailed. This is a very good book for its target audience.” (W. Miller Jr., Zentralblatt MATH, Vol. 1175, 2010)“The goal of the book under review is to teach group theory in close connection to applications. … Every chapter of the book finishes with several selected problems. Specific to this book is the feature that every abstract theoretical group concept is introduced and applied in a concrete physical way. This is why the book is very useful for anyone interested in applications of group theory to the wide range of condensed matter phenomena.” (Oktay K. Pashaev, Mathematical Reviews, Issue 2010 i)“It is highly welcomed because of its well-thought structuring and the plenty of non-trivial examples. The authors develop those parts of the theory of groups which are interesting for physicists, from chapter to chapter offering nearly at any step one or more informative application.” (G. Kowol, Monatshefte für Mathematik, Vol. 157 (2), June, 2009)Table of ContentsBasic Mathematics.- Basic Mathematical Background: Introduction.- Representation Theory and Basic Theorems.- Character of a Representation.- Basis Functions.- Introductory Application to Quantum Systems.- Splitting of Atomic Orbitals in a Crystal Potential.- Application to Selection Rules and Direct Products.- Molecular Systems.- Electronic States of Molecules and Directed Valence.- Molecular Vibrations, Infrared, and Raman Activity.- Application to Periodic Lattices.- Space Groups in Real Space.- Space Groups in Reciprocal Space and Representations.- Electron and Phonon Dispersion Relation.- Applications to Lattice Vibrations.- Electronic Energy Levels in a Cubic Crystals.- Energy Band Models Based on Symmetry.- Spin–Orbit Interaction in Solids and Double Groups.- Application of Double Groups to Energy Bands with Spin.- Other Symmetries.- Time Reversal Symmetry.- Permutation Groups and Many-Electron States.- Symmetry Properties of Tensors.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Synergetics: Introduction and Advanced Topics
Book SynopsisThis book is an often-requested reprint of two classic texts by H. Haken: "Synergetics. An Introduction" and "Advanced Synergetics". Synergetics, an interdisciplinary research program initiated by H. Haken in 1969, deals with the systematic and methodological approach to the rapidly growing field of complexity. Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made. This may well explain the timelessness of H. Haken's original texts on this topic, which are now recognized as landmarks in the field of complex systems. They provide both the beginning graduate student and the seasoned researcher with solid knowledge of the basic concepts and mathematical tools. Moreover, they admirably convey the spirit of the pioneering work by the founder of Synergetics through the essential applications contained herein that have lost nothing of their paradigmatic character since they were conceived.Table of ContentsAn Introduction.- Advanced Topics.
£85.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Mechanics: Symbolism of Atomic Measurements
Book SynopsisA unique legacy, these lecture notes of Schwinger’s course held at the University of California at Los Angeles were carefully edited by his former collaborator Berthold-Georg Englert and constitute both a self-contained textbook on quantum mechanics and an indispensable source of reference on this fundamental subject by one of the foremost thinkers of twentieth century physics.Trade ReviewFrom the reviews: "Quantum Mechanics: Symbolism of Atomic Measurements is not just another textbook on quantum mechanics. Rather, it contains truly novel elements of both content and style. In particular, Schwinger begins his treatment not with de Broglie waves or the Schrödinger equation but rather with the measurement process. His idea is to derive, or at least make plausible, the formalism of state vectors, bras and kets, by reference to quantum measurements such as the Stern-Gerlach experiment. This [...] is simply the basis of a new way of teaching quantum mechanics. This opening chapter should be of interest to all scholars of quantum theory and might form a new topic of research for philosophers of quantum mechanics." (Contemporary Physics, 44/2, 2003) "There are dozen of excellent textbooks on the market. But this one really is different." (T. Kibble, The Times Higher Education Supplement, 2001) "The material covered is superficially similar to that of a typical graduate quantum mechanics course [...] However, each chapter has beautiful and unusual treatments of familiar topics. [...] This book would make an outstanding supplement and reference for a graduate quantum mechanics course. Theoretical physicists will delight in this wonderful book, which should be available in the library system of any institution with a research or graduate program in physics. Graduate students through professionals." (CHOICE, Dec. 2001) "The book is a tour-de-force. Once the groundwork is laid, he goes into subjects with the mathematical virtuosity for which he was famous – not advanced mathematics, but the incredible use of simple mathematics. … there are gems throughout the book. … it is a wonderful book for a professor to own, like Feyman’s lectures, because there is so much to learn from it. … The book was lovingly edited from some UCLA lecture notes, by Berthold-Georg Englert, a longtime student and assistant of Schwinger’s … ." (Daniel Greenberger, American Journal of Physics, Vol 71 (9), 2003) "Editor Englert has performed a service for physicists everywhere by making available this book, which is based on Schwinger’s unpublished UCLA lecture notes. … each chapter has beautiful and unusual treatments of familiar topics. … There are excellent problems at the end of each chapter. This book would make an outstanding supplement and reference for a graduate quantum mechanics course. Theoretical physicists will delight in this wonderful book, which should be available in the library system of any institution with a research or graduate program … ." (M. C. Ogilvie, CHOICE, December, 2001) "The book commences with an absorbing prologue in which Schwinger talks us through the development of quantum mechanic and quantum field theory in an easy conversational style. … The book is packed with exercises for the reader to attempt. … Anyone who works religiously through these exercises will acquire a thoroughly adequate command of quantum mechanics." (W. Cox, Mathematical Reviews, Issue 2002 h) "Quantum mechanics: Symbolism of Atomic Measurements is not just another textbook on quantum mechanics. Rather, it contains truly novel elements of both content and style. … This opening chapter should be of interest to all scholars of quantum theory and might form a new topic of research for philosophers of quantum mechanics. Throughout the text, new material is presented at a breathless pace. All the usual elements of the subject are there, but Schwinger’s presentation reveals surprises in even the most familiar of these." (S. M. Barnett, Contemporary Physics, Vol. 44 (2), 2003) "In the beginning, the editor has added an important material in the form of a prologue … . This is one of the best treatments of the philosophy of quantum mechanics, which I have come across. … One of the major features of the book is the incorporation of a large number of problems … . the contents of the problems are well integrated in the text and have become part of it. This has caused a rich and tight structure of the logical arguments." (S. S. Bhattacharyya, Indian Journal of Physics, Vol. 76B (3), 2002) "This unique textbook is based upon the lecture notes that Julian Schwinger wrote up for the students of the quantum mechanics course … . this book would probably make an ideal quantum mechanics reference … . There are a large number of problems included at the end of each chapter, which comprise an excellent resource for any lecturer … . this textbook is a unique resource, which provides an insight into the thoughts and deliberations of one of this century’s giants of quantum mechanics." (P. C. Dastoor, The Physicist, Vol. 38 (5), 2001) "There are dozens of excellent textbooks on the market. But this one really is different. … there is a carefully argued historical and philosophical prologue that sets the scene, centred on the two key features of quantum physics – atomicity and its probabilistic character; this alone would make the book worthwhile. The emphasis on discrete variables is a very modern approach… . To a theoretical physicist, this book is a delight and a wonderful resource. … This is a book I shall treasure." (Tom Kibble, Times Higher Education Supplement, September, 2001)Table of ContentsPrologue.- A. Fall Quarter: Quantum Kinematics.- 1 Measurement Algebra.- 2 Continuous q, p Degree of Freedom.- 3 Angular Momentum.- 4 Galilean Invariance.- B. Winter Quarter: Quantum Dynamics.- 5 Quantum Action Principle.- 6 Elementary Applications.- 7 Harmonic Oscillators.- 8 Hydrogenic Atoms.- C. Spring Quarter: Interacting Particles.- 9 Two-Particle Coulomb Problem.- 10 Identical Particles.- 11 Many-Electron Atoms.- 12 Electromagnetic Radiation.
£52.24
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Statistical Physics: An Advanced Approach with
Book SynopsisThe book is divided into two parts. The first part looks at the modeling of statistical systems before moving on to an analysis of these systems. This second edition contains new material on: estimators based on a probability distribution for the parameters; identification of stochastic models from observations; and statistical tests and classification methods.Table of Contents1 Statistical Physics: Is More than Statistical Mechanics.- I Modeling of Statistical Systems.- 2 Random Variables: Fundamentals of Probability Theory and Statistics.- 3 Random Variables in State Space: Classical Statistical Mechanics of Fluids.- 4 Random Fields: Textures and Classical Statistical Mechanics of Spin Systems.- 5 Time-Dependent Random Variables: Classical Stochastic Processes.- 6 Quantum Random Systems.- 7 Changes of External Conditions.- II Analysis of Statistical Systems.- 8 Estimation of Parameters.- 9 Signal Analysis: Estimation of Spectra.- 10 Estimators Based on a Probability Distribution for the Parameters.- 11 Identification of Stochastic Models from Observations.- 12 Estimating the Parameters of a Hidden Stochastic Model.- 13 Statistical Tests and Classification Methods.- Appendix: Random Number Generation for Simulating Realizations of Random Variables.- Problems.- Hints and Solutions.- References.
£66.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Percolation
Book SynopsisPercolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. Much new material appears in this second edition including dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.Table of Contents1 What is Percolation?.- 2 Some Basic Techniques.- 3 Critical Probabilities.- 4 The Number of Open Clusters per Vertex.- 5 Exponential Decay.- 6 The Subcritical Phase.- 7 Dynamic and Static Renormalization.- 8 The Supercritical Phase.- 9 Near the Critical Point: Scaling Theory.- 10 Near the Critical Point: Rigorous Results.- 11 Bond Percolation in Two Dimensions.- 12 Extensions of Percolation.- 13 Percolative Systems.- Appendix I. The Infinite-Volume Limit for Percolation.- Appendix II. The Subadditive Inequality.- List of Notation.- References.- Index of Names.
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Field Theory in Condensed Matter Physics
Book SynopsisThis is an approachable introduction to the important topics and recent developments in the field of condensed matter physics. First, the general language of quantum field theory is developed in a way appropriate for dealing with systems having a large number of degrees of freedom. This paves the way for a description of the basic processes in such systems. Applications include various aspects of superfluidity and superconductivity, as well as a detailed description of the fractional quantum Hall liquid.Table of ContentsQuantum Mechanics and Fundamentals of Quantum Field Theory.- Path Integral Quantization.- Broken Symmetry and Phase Transition.- Some Applications - Warming Ups.- Superconductivity.- Quantum Hall Liquids and Chern--Simons Gauge Field.- Appendix.
£132.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Heat Kernel and Quantum Gravity
Book SynopsisThis book is aimed at theoretical as well as primarily physicists graduate students in field working quantum theory, quantum gravity, theories, gauge to sdme and and, it is not extent, general relativity cosmology. Although aimed at a I that it also be of level, hope in mathematically rigorous may terest to mathematical and mathematicians in physicists working spectral of differential mani geometry, spectral asymptotics on operators, analysis differential and mathematical methods in folds, geometry quantum theory. Thisbook will be considered too abstract some but certainly by physicists, not detailed and most mathematicians. This in completeenoughby means, thatthe material is at the level of particular, presented "physical" So, rigor. there theorems and areno and technicalcalculationsare lemmas, proofs long omitted. I tried detailed to a ofthe basic Instead, give presentation ideas, methodsandresults. Itried makethe to as andcom Also, exposition explicit as the lessabstractandhaveillustratedthe plete possible, methods language and results withsome As is well "onecannot examples. known, cover every in an text. The in this thing", especially introductory approach presented book the lines is a further of the so called along goes (and development) fieldmethod ofDe Witt. As a Ihavenot dealt at background consequence, allwithmanifoldswith boundary,non Laplacetype (ornonminimal) opera Riemann Cartan manifolds well with as as recent tors, developments many and advanced such Ashtekar's more as topics, approach,supergravity,strings, matrix etc. The membranes, interested reader is referred models, M theory tothe literature.Trade Review"This monograph rightly belongs to a series ‘Lecture notes in Physics’, as it represents a well-written review of main results by the author, who is a recognized expert on heat kernel techniques in quantum gravity. [...] The results exposed in this book reflect the major contributions of the author to differential geometry and the theory of differential operators. They have many applications in quantum field theory with background fields, and indeed, the book can be used as a text for a short graduate course in the heat kernel techniques and their quantum gravity." (Mathematical Reviews 2003a)Table of ContentsBackground Field Method in Quantum Field Theory.- Technique for Calculation of De Witt Coefficients.- Partial Summation of Schwinger-De Witt Expansion.- Higher-Derivative Quantum Gravity.- Conclusion.
£85.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Geometry of Minkowski Space-Time
Book SynopsisThis book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry.The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions.The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time.Moreover, from this formalization the understanding of gravity comes as a manifestation of curvature of space-time, suggesting new research fields.Table of ContentsIntroduction.- Hyperbolic Numbers.- Geometrical Representation of Hyperbolic Numbers.- Trigonometry in the Hyperbolic (Minkowski) Plane.- Equilateral Hyperbolas and Triangles in the Hyperbolic Plane.- The Motions in Minkowski Space-Time (Twin Paradox).- Some Final Considerations.
£47.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Field Theory III: Gauge Theory: A Bridge between Mathematicians and Physicists
Book SynopsisIn this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a ParadigmPart II: Ariadne's Thread in Gauge TheoryPart III: Einstein's Theory of Special RelativityPart IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos). Trade ReviewFrom the reviews:“This book is the third volume of a complete exposition of the important mathematical methods used in modern quantum field theory. It presents the very basic formalism, important results, and the most recent advances emphasizing the applications to gauge theory. … the book’s greatest strength is Zeidler’s zeal to help students understand fundamental mathematics better. I thus find the book extremely useful since it signifies the role of mathematics for the road to reality … .” (Gert Roepstorff, Zentralblatt MATH, Vol. 1228, 2012)“The present book is a good companion to the literature on the subject of the volume title, especially for those already familiar with it. … the book touches upon a large number of subjects on the interface between mathematics and physics, providing a good overview of gauge theory in both fields. It contains lots of background material, many historical remarks, and an extensive bibliography that helps the interested reader to continue his or her more thorough studies elsewhere.” (Walter D. van Suijlekom, Mathematical Reviews, Issue 2012 m)Table of ContentsPrologue.- Part I. The Euclidean Manifold as a Paradigm: 1. The Euclidean Space E3 (Hilbert Space and Lie Algebra Structure).- 2. Algebras and Duality (Tensor Algebra, Grassmann Algebra, Cli_ord Algebra, Lie Algebra).- 3. Representations of Symmetries in Mathematics and Physics.- 4. The Euclidean Manifold E3.- 5. The Lie Group U(1) as a Paradigm in Harmonic Analysis and Geometry.- 6. Infinitesimal Rotations and Constraints in Physics.- 7. Rotations, Quaternions, the Universal Covering Group, and the Electron Spin.- 8. Changing Observers - A Glance at Invariant Theory Based on the Principle of the Correct Index Picture.- 9. Applications of Invariant Theory to the Rotation Group.- 10. Temperature Fields on the Euclidean Manifold E3.- 11. Velocity Vector Fields on the Euclidean Manifold E3.- 12. Covector Fields and Cartan's Exterior Differential - the Beauty of Differential Forms.- Part II. Ariadne's Thread in Gauge Theory: 13. The Commutative Weyl U(1)-Gauge Theory and the Electromagnetic Field.- 14. Symmetry Breaking.- 15. The Noncommutative Yang{Mills SU(N)-Gauge Theory.- 16. Cocycles and Observers.- 17. The Axiomatic Geometric Approach to Bundles.- Part III. Einstein's Theory of Special Relativity: 18. Inertial Systems and Einstein's Principle of Special Relativity.- 19. The Relativistic Invariance of the Maxwell Equations.- 20. The Relativistic Invariance of the Dirac Equation and the Electron Spin.- Part IV. Ariadne's Thread in Cohomology: 21. The Language of Exact Sequences.- 22. Electrical Circuits as a Paradigm in Homology and Cohomology.- 23. The Electromagnetic Field and the de Rham Cohomology.- Appendix.- Epilogue.- References.- List of Symbols.- Index
£189.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG 3+1 Formalism in General Relativity: Bases of
Book SynopsisThis graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.Trade ReviewFrom the reviews:“The monograph originating from lectures is devoted to the 3+1 formalism in general relativity. It starts with three chapters on basic differential geometry, the geometry of single hypersurfaces embedded in space-time, and the foliation of space-time by a family of spacelike hypersurfaces. … With the attempt to make the text self-consistent and complete, the calculations are … detailed such that the book is well suitable for undergraduate and graduate students.” (Horst-Heino von Borzeszkowski, Zentralblatt MATH, Vol. 1254, 2013)“This book is written for advanced students and researchers who wish to learn the mathematical foundations of various approaches that have been proposed to solve initial value problems (with constraints) for the Einstein equations numerically. … Even for experts it may be useful, as it includes an extensive bibliography up to 2011.” (Hans-Peter Künzle, Mathematical Reviews, January, 2013)Table of ContentsBasic Differential Geometry.- Geometry of Hypersurfaces.- Geometry of Foliations.- 3+1 decomposition of Einstein Equation.- 3+1 Equations for Matter and Electromagnetic Field.- Conformal Decompositon.- Asymptotic Flatness and Global Quantities.- The Initial Data Problem.- Choice of Foliation and Spatial Coordiinates.- Evolution Schemes.- Conformal Killing Operator and Conformal Vector Laplacian.- Sage Codes.
£47.49
Springer Fachmedien Wiesbaden Grundkurs Theoretische Physik 6: Statistische
Book SynopsisDer Grundkurs Theoretische Physik deckt in 7 Bänden alle für das Diplom und für Bachelor/Master-Studiengänge maßgeblichen Gebiete ab. Jeder Band vermittelt das im jeweiligen Semester notwendige theoretisch-physikalische Rüstzeug. Übungsaufgaben mit ausführlichen Lösungen dienen der Vertiefung des Stoffs. Der 6. Band zur Statistischen Physik wurde für die Neuauflage grundlegend überarbeitet und um aktuelle Entwicklungen ergänzt. Durch die zweifarbige Gestaltung ist der Stoff jetzt noch übersichtlicher gegliedert.Table of ContentsKlassische statistische Physik.- Quantenstatistik.- Quantengase.- Phasenübergänge.- Lösungen der Übungsaufgaben.
£47.49
Springer Fachmedien Wiesbaden Grundkurs Theoretische Physik 5/1:
Book SynopsisDer Grundkurs Theoretische Physik deckt in 7 Bänden die im Diplom- und Bachelor/Master-Studium maßgeblichen Gebiete ab und vermittelt das im jeweiligen Semester benötigte theoretisch-physikalische Rüstzeug. Der erste Teil von Band 5 beginnt mit einer Begründung der Quantenmechanik und der Zusammenstellung ihrer formalen Grundlagen, um dann Konzepte und Begriffsbildungen an Modellsystemen zu illustrieren. Der Band enthält Übungsaufgaben und Kontrollfragen zur Vertiefung des Stoffs. Die überarbeitete und ergänzte Neuauflage ist zweifarbig gestaltet.Table of ContentsInduktive Begründung der Wellenmechanik.- Schrödinger-Gleichung.- Grundlagen der Quantenmechanik (Dirac-Formalismus).- Einfache Modellsysteme.- Lösungen der Übungsaufgaben.
£36.09
Springer Fachmedien Wiesbaden Praktische Mathematik mit MATLAB, Scilab und
Book SynopsisDer Band bietet eine Schritt-für-Schritt-Einführung in das numerische Rechnen mit den Programmen MATLAB, Scilab und Octave. Anhand zahlreicher Beispiele zeigen die Autoren, wie die mathematischen Tools zur Lösung mathematischer, physikalischer und insbesondere ingenieurwissenschaftlicher Aufgaben eingesetzt werden können. Dazu gehören die Lösung von linearen Gleichungssystemen, nichtlinearen Gleichungen und Differentialgleichungen, die Fourier- und Wavelet-Transformation, Kurvenanpassung und Interpolation sowie die numerische Integration.Trade Review“... Zum Nachschlagen enthält jedes Kapitel eine Zusammenfassung, und ganz am Ende stehen einige Testfragen sowie eine kleine Literaturliste, so dass sich der neugierige Leser weiteres Futter verschaffen kann. ... erkunden die Autoren einige Teilbereiche der numerischen Mathematik, die für Anfänger geeignet sind. ... Die vielen Beispiele und Aufgaben unterstützen den Leser enorm ... Wer sich für das Lösen numerischer Probleme mit zeitgemäßen Werkzeugen interessiert, der kann zunächst bedenkenlos zu diesem Werk greifen.” (Harald Löwe, in: Mathematische Semesterberichte, Jg. 62, 2015, S. 114 f.) Table of Contents
£37.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Chromodynamics on the Lattice: An Introductory Presentation
Book SynopsisQuantum chromodynamics (QCD) is the fundamental quantum ?eld theory of quarks and gluons. In order to discuss it in a mathematically well-de?ned way, the theory has to be regularized. Replacing space-time by a Euclidean lattice has proven to be an e?cient approach which allows for both theor- ical understanding and computational analysis. Lattice QCD has become a standard tool in elementary particle physics. Asthetitlealreadysays:thisbookisintroductory!Thetextisintendedfor newcomerstothe?eld,servingasastartingpoint.Wesimplywantedtohavea bookwhichwecanputintothehandsofanadvancedstudentfora?rstreading on lattice QCD. This imaginary student brings as a prerequisite knowledge of higher quantum mechanics, some continuum quantum ?eld theory, and basic facts of elementary particle physics phenomenology. In view of the wealth of applications in current research the topics p- sented here are limited and we had to make some painful choices. We discuss QCD but omit most other lattice ?eld theory applications like scalar th- ries, gauge-Higgs models, or electroweak theory. Although we try to lead the reader up to present day understanding, we cannot possibly address all on- ing activities, in particular concerning the role of QCD in electroweak theory. Subjects like glueballs, topological excitations, and approaches like chiral p- turbation theory are mentioned only brie?y. This allows us to cover the other topics quite explicitly, including detailed derivations of key equations. The ?eld is rapidly developing. The proceedings of the annual lattice conferences provide information on newer directions and up-to-date results.Trade ReviewFrom the reviews:“This is a very nice and readable book on lattice gauge theories. It is conceived for non-specialists in the field and is quite self-contained. … It is a modern, updated introduction to lattice gauge theory, very easy to consult and conceived in a modern way. This is an excellent textbook for students or anyone wishing to be introduced to the subject.” (Giuseppe Nardelli, Mathematical Reviews, Issue 2010 k)Table of ContentsThe path integral on the lattice.- The path integral on the lattice.- QCD on the lattice — a first look.- QCD on the lattice — a first look.- Pure gauge theory on the lattice.- Pure gauge theory on the lattice.- Numerical simulation of pure gauge theory.- Numerical simulation of pure gauge theory.- Fermions on the lattice.- Fermions on the lattice.- Hadron spectroscopy.- Hadron spectroscopy.- Chiral symmetry on the lattice.- Chiral symmetry on the lattice.- Dynamical fermions.- Dynamical fermions.- Symanzik improvement and RG actions.- Symanzik improvement and RG actions.- More about lattice fermions.- More about lattice fermions.- Hadron structure.- Hadron structure.- Temperature and chemical potential.- Temperature and chemical potential.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Die Relativitätstheorie Einsteins
Book SynopsisDieses Buch ist bis heute eine der populärsten Darstellungen der Relativitätstheorie geblieben. In der vorliegenden Version haben J. Ehlers und M. Pössel vom Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) in Golm/Potsdam den Bornschen Text kommentiert und einen den anschaulichen, aber präzisen Stil Borns wahrendes, umfangreiches Ergänzungskapitel hinzugefügt, das die stürmische Entwicklung der Relativiatätstheorie bis hin zu unseren Tagen nachzeichnet. Eingegangen wird auf Gravitationswellen und Schwarze Löcher, auf neuere Entwicklungen der Kosmologie, auf Ansätze zu einer Theorie der Quantengravitation und auf die zahlreichen raffinierten Experimente, welche die Gültigkeit der Einsteinschen Theorie mit immer größerer Genauigkeit bestätigt haben. Damit bleibt dieses Buch nach wie vor einer der unmittelbarsten Zugänge zur Relativitätstheorie für alle die sich für eine über das rein populärwissenschaftliche hinausgehende Einführung interessieren.Trade Review"Allen interessierten Laien sehr zu empfehlen, die ohne höhere Mathematik tiefer in diese Materie eindringen möchten." (Weltraum-Facts mit Space-Informer, 2001) "Alle, die sich über eine rein populärwissenschaftliche Einführung hinaus für die Relativitätstheorie interessieren – besonders Physikstudenten – werden an dem eingehenden Werk Freude haben." (Der Sternenbote, 2001) "Die Erweiterung bereichert den Text von Born aber nicht nur um neuere Entwicklungen der Physik. Rückverweise verzahnen die neuen Kapitel inhaltlich mit den vorstehenden Überlegungen, und auch das Bornsche Projekt, für den mit Schulmathemaitk und einem "gesunden Menschenverstand" ausgestatteten Leser verständlich zu sein, wird erfolgreich fortgeführt." (Wissenschaftlicher Literaturanzeiger, 2001) "Das Buch zeichnet sich in besonderm Maße gegenüber fast allen anderen Abhandlungen über dieses Thema dadurch aus, daß es in einer zuweilen geradezu brillianten Ausdrucksweise die Problematik der klassischen Physik und deren Hintergrund aufzeigt, die dann durch Einsteins Theorien eine Auflösung fand. [...] Alles in allem ein sehr lesenswertes Buch, jedoch kein populärwissenschaftliches und für den Laien sicherlich auch kein leichtes. Denn trotz der außerordentlich gut verständlichen Darstellungsweise Borns erfordert das Buch außer etwas Grundlagen-Mathematik ein hohes Maß an Aufmerksamkeit und die bereitschaft, physikalsiche Sachverhalte gedanklich zu durchdringen. Es ist mit sicherheit ein Verdienst von Herausgebern und Verlag, Borns Buch durch die Neuauflage mit den aktuellen Ergänzungen wieder einer interessierten Leserschaft verfügbar zu machen." (Nachrichten der Olbers-Gesellschaft, 2001) "Wer eine fundierte, gründliche Einführung in die Welt der Relativitätstheorie sucht, kommt an Borns Klassiker nicht vorbei. Freilich muß man sich mitunter bemühen und auch einiges an Mathematik bewältigen, läuft dafür aber nicht Gefahr, durch aus dem Alltag entlehnte Analogien verwirrt zu werden." (Sirius – Zeitschrift der Vereinigten Amateur-Astronomen, 2002) "Wer die populärwissenschaftlichen Darstellungen der Relativitätstheorie als nicht ausreichend betrachtet und gern etwas tiefer schürfen möchte, dem sei dieses Buch als Lektüre ans Herz gelegt." (Astrokurier, 2002) "Ehlers und Pössel ist damit ein gelungenes Remake von Borns wegweisendem Werk gelungen. Sie haben bewiesen, dass der 80 Jahre alte Zugang zu Einsteins Theorie auch heute noch gangbar ist." (Physik in unserer Zeit, 2002) "[...] weiterhin einer der unmittelbarsten Zugänge zur Relativitätstheorie für Schüler-, Lehrer- und Studentenschaft sowie für alle, die sich nicht beruflich mit relativistischer Physik beschäftigen möchten, insbesondere für jene Leserschaft aus der Amateur-Astronomie, die an einem tieferen Verständnis dieses spannenden Themas interessiert ist. Gerade diesem Kreis ist das vorliegende Buch als Einführung in die moderne Kosmologie sehr zu empfehlen." (ORION 61/314, 2003)Table of ContentsGeometrie und Kosmologie.- Die Grundgesetze der klassischen Mechanik.- Das Newtonsche Weltsystem.- Die Grundgesetze der Optik.- Die Grundgesetze der Elektrodynamik.- Das spezielle Einsteinsche Relativitätsprinzip.- Die allgemeine Relativitätstheorie Einsteins.- Neuere Entwicklungen der relativistischen Physik.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers II: PDE, SDE, Diffusions, Random
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012. Volume II includes the papers on PDE, SDE, diffusions, and random media.Table of ContentsVol. II: Diffusion processes with continuous coefficients - I (with D. W. Stroock).- Diffusion processes with continuous coefficients - II (with D. W. Stroock).- Diffusion processes with boundary conditions (with D. W. Stroock).- On degenerate elliptic-parabolic operators of second order and their associated diffusions (with D. W. Stroock).- On the support of diffusion processes with applications to the strong maximum principle (with D. W. Stroock).- Diffusion processes (with D. W. Stroock).- A probabilistic approach to Hp(Rd) (with D. W. Stroock).- Kac functional and Schrodinger equation (with K. L. Chung).- Brownian motion in a wedge with oblique reection (with R. J. Williams).- A multidimensional process involving local time (with A.S. Sznitman).- Etat fondamental et principe du maximum pour les operateurs elliptiques du second ordre dans des domaines generaux. [The ground state and maximum principle for second-order elliptic operators in general domains] (with H. Berestycki and L. Nirenberg).- The principal eigenvalue and maximum principle for second-order elliptic operators in general domains (with H. Berestycki and L. Nirenberg).- Diffusion semigroups and di_usion processes corresponding to degenerate divergence form operators (with J. Quastel).- Random Media.- Diffusion in regions with many small holes (with G. Papanicolaou).- Boundary value problems with rapidly oscillating random coefficients (with G. Papanicolaou).- Diffusions with random coefficients (with G. Papanicolaou).- Ohrnstein-Uhlenbeck process in a random potential (with G. Papanicolaou).- Large deviations for random walks in a random environment.- Random walks in a random environment.- Stochastic homogenization of Hamilton-Jacobi-Bellman equations (with E. Kosygina and F. Rezakhanlou).- Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium (with E. Kosygina).- Behavior of the solution of a random semilinear heat equation (with N. Zygouras).
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers III: Large Deviations
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012.Volume III includes the papers on large deviations. Table of ContentsLarge Deviations.- Asymptotic probabilities and differential equations.- On the behavior of the fundamental solution of the heat equation with variable coefficients .- Diffusion processes in a small time interval .- On a variational formula for the principal eigenvalue for operators with maximum principle.- Asymptotic evaluation of certain Markov process expectations for large time I.- Asymptotic evaluation of certain Markov process expectations for large time II.- Asymptotic evaluation of certain Wiener integrals for large time.- Asymptotics for the Wiener sausage.- Erratum: Asymptotics for the Wiener sausage.- Asymptotic evaluation of certain Markov process expectations for large time III.- On the principal eigenvalue of second-order elliptic differential operators.- On laws of the iterated logarithm for local times.- Some problems of large deviations.- On the number of distinct sites visited by a random walk.- A law of the iterated logarithm for total occupation times of transient Brownian motion.- Some problems of large deviations .- The polaron problem and large deviations.- Asymptotic evaluation of certain Markov process expectations for large time IV.- Asymptotics for the polaron.- Large deviations for stationary Gaussian processes.- Large deviations and applications.- Large deviations for non-interacting infinite-particle systems.- Some familiar examples for which the large deviation principle does not hold.- The large deviation principle for the Erdös-Rényi random graph.- Large deviations for random matrices.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers IV: Particle Systems and Their
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012. Volume IV includes the papers on particle systems.Table of ContentsVolume 4: Particle Systems and Their Large Deviations.- Nonlinear diffusion limit for a system with nearest neighbor interaction.- Hydrodynamics and large deviation for simple exclusion processes.- Large deviations from a hydrodynamic scaling limit.- On the derivation of conservation laws for stochastic dynamics.- Scaling limits for interacting diffusions.- Scaling limit for interacting Ornstein-Uhlenbeck processes.- Entropy methods in hydrodynamical scaling.- Hydrodynamical limit for a Hamiltonian system with weak noise.- Nonlinear diffusion limit for a system with nearest neighbor interactions II.- Regularity of self-diffusion coefficient.- Entropy methods in hydrodynamic scaling.- Spectral gap for zero-range dynamics.- The complex story of simple exclusion.- Non-gradient models in hydrodynamic scaling.- Relative entropy and mixing properties of interacting particle systems.- Diffusive limit of lattice gas with mixing conditions.- Large deviations for the symmetric simple exclusion process in dimensions d > 3.- Large deviations for interacting particle systems.- Infinite particle systems and their scaling limits.- Lectures on hydrodynamic scaling.- Scaling limits of large interacting systems .- Asymptotic behavior of a tagged particle in simple exclusion processes.- Large deviation and hydrodynamic scaling.- Symmetric simple exclusion process: regularity of the self-diffusion coefficient.- Finite-dimensional approximation of the self-diffusion coefficient for the exclusion process.- Large deviations for the asymmetric simple exclusion process.- Diffusive behaviour of the equilibrium fluctuations in the asymmetric exclusion processes.- On viscosity and fluctuation-dissipation in exclusion processes.- Large deviations for the current and tagged particle in 1d nearest neighbor.- Symmetric simple exclusion.- List of Publications of S.R.S. Varadhan.- Acknowledgements.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Basic Algebraic Geometry 1: Varieties in Projective Space
Book SynopsisShafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles.Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field.Trade Review“This is a very good book and very good introduction to algebraic geometry and it serves an entry door to this enormous subject in mathematics. … This book is classical and I strongly recommend it as the first book on algebraic geometry. … It is an excellent book and every mathematician should have a copy.” (Philosophy, Religion and Science Book Reviews, Bookinspections.wordpress.com, July, 2016)“I find the book wonderfully put together, and I am sure the reader will learn a lot, either from systematic study or from browsing particular topics. … In each chapter, the theorems, propositions, corollaries, examples, remarks, etc., each have their own independent numbering system, running consecutively throughout the chapter. This makes it a real chore to track any internal reference in the book.” (Robin Hartshorne, SIAM Review, Vol. 56 (4), December, 2014)“The author’s two-volume textbook ‘Basic Algebraic Geometry’ is one of the most popular standard primers in the field. … the author’s unique classic is a perfect first introduction to the geometry of algebraic varieties for students and nonspecialists, and the current, improve third edition will maintain this outstanding role of the textbook in the relevant literature without any doubt.” (Werner Kleinert, zbMATH, Vol. 1273, 2013)Table of ContentsPreface.- Book 1. Varieties in Projective Space: Chapter 1. Basic Notions.- Chapter II. Local Properties.- Chapter III. Divisors and Differential Forms.- Chapter IV. Intersection Numbers.- Algebraic Appendix.- References.- Index
£75.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Springer Handbook of Spacetime
Book SynopsisThe Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects.The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.Trade Review“This is a complete comprehensive textbook of all areas of classical and relativistic Physics including mechanics, E & M, quantum theory, perturbation, solid state, and particle physics. … It is good enough to be read cover to cover and will not disappoint the reader reviewer. I highly recommend this book for physics students, and investigators in physics theories.” (Joseph J. Grenier, Amazon.com, January, 2016)“This is a splendid and very comprehensive review of the special and general theories of relativity and their applications, in a collection of about 40 articles by experts in the field. … the book will appeal to a wide variety of readers, from advanced undergraduates to experts in the field. … I doubt that there is any physicist who would not find something new and interesting here.” (Alan Heavens, The Observatory, Vol. 135 (1245), April, 2015)Table of ContentsPreface (A. Ashtekar, V. Petkov).- Part A – Introduction to Spacetime Structure.- Chap. 1 From Aether Theory to Special Relativity.- Chap. 2 The Historical Origins of Spacetime.- Chap. 3 Relativity Today.- Chap. 4 Acceleration and Gravity: Einstein's Principle.- Chap. 5 The Geometry of Newton's and Einstein's Theories.- Part B – Foundational Issues.- Chap. 6 Time in Special Relativity.- Chap. 7 Rigid Motion and Adapted Frames.- Chap. 8 Physics as Spacetime Geometry.- Chap. 9 Electrodynamics of Radiating Charges.- Chap. 10 The Nature and Origin of Time-Asymmetric Spacetime Structures.- Chap. 11 Teleparallelism: A new Insight into Gravity.- Chap. 12 Gravity and the Spacetime: An Emergent Perspective.- Chap. 13 Spacetime and the Passage of Time.- Part C – Spacetime Structure and Mathematics.- Chap. 14 Unitary Representations of the Inhomogeneous Lorentz Group and Their Significance in Quantum Physics.- Chap. 15 Spinors.- Chap. 16 The Initial Value Problem in General Relativity.- Chap. 17 Dynamical and Hamiltonian Formulation of General Relativity.- Chap. 18 Positive Energy Theorems in General Relativity.- Chap. 19 Conserved Charges in Asymptotically (Locally) AdS Spacetimes.- Chap. 20 Spacetime Singularities.- Chap. 21 Singularities in Cosmological Spacetimes.- Part D – Confronting Relativity theories with observations.- Chap. 22 The experimental status of Special and General Relativity Chap. 23. Observational Constraints on Local Lorentz Invariance.- Chap. 24 Relativity in GNSS.- Chap. 25 Quasi Local Black Hole Horizons.- Chap. 26 Gravitational Astronomy.- Chap. 27 Probing Dynamical Spacetimes with Gravitational Waves.- Part E – General Relativity and the Universe.- Chap. 28 Einstein's Equation, Cosmology and Astrophysics.- Chap. 29 Viscous Universe Models.- Chap. 30 Friedmann-Lemaitre-Robertson-Walker Cosmology.- Chap. 31 Exact Approach to Inflationary Universe Models.- Chap. 32 Cosmology with the Cosmic Microwave Background.- Part F – Spacetime Beyond Einstein.- Chap. 33 Quantum Gravity.- Chap. 34 Quantum Gravity via Causal Dynamical Triangulations.- Chap. 35 String Theory and Primordial Cosmology.- Chap. 36 Quantum Spacetime.- Chap. 37 Gravity, Geometry and the Quantum.- Chap. 38 Spin Foams.- Chap. 39 Loop Quantum Cosmology.- Acknowledgements.- About the Authors.- Subject Index.
£251.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Concepts and Results in Chaotic Dynamics: A Short Course
Book SynopsisThe study of dynamical systems is a well established field. This book provides a panorama of several aspects of interest to mathematicians and physicists. It collects the material of several courses at the graduate level given by the authors, avoiding detailed proofs in exchange for numerous illustrations and examples. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.Trade ReviewFrom the reviews: "The book is a good introduction to the field of dynamical systems with a particular emphasis on statistical properties and applications. In particular, the relations both with real experiments with numerical simulations are discussed. … The book contains many figures that really help the understanding of the text. The book can be used as a text for an introductory course in dynamical systems (at the master’s or Ph.D. level). It is particularly suited for students with interests in applications (either physics, economy or biology)." (Carlangelo Liverani, Mathematical Reviews, Issue 2007 m) "Two thoughts crossed my mind when I picked up this book. The first was: ‘what a physically attractive book.’ The second was: ‘what a short book to have on such a wide ranging topic.’ … It is a perfect size to carry in a knapsack, the print is clear and the layout of text, equations, and figures is marvelously done. … images are multi-colored stereo images, and allow the reader to ‘see’ a three dimensional effect that helps illustrate the phenomena." (David S. Mazel, MathDL, December, 2007)Table of ContentsA Basic Problem.- Dynamical Systems.- Topological Properties.- Hyperbolicity.- Invariant Measures.- Entropy.- Statistics and Statistical Mechanics.- Other Probabilistic Results.- Experimental Aspects.
£40.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Statistical Physics: An Advanced Approach with Applications
Book SynopsisThe application of statistical methods to physics is essential. This unique book on statistical physics offers an advanced approach with numerous applications to the modern problems students are confronted with. Therefore the text contains more concepts and methods in statistics than the student would need for statistical mechanics alone. Methods from mathematical statistics and stochastics for the analysis of data are discussed as well. The book is divided into two parts, focusing first on the modeling of statistical systems and then on the analysis of these systems. Problems with hints for solution help the students to deepen their knowledge. The third edition has been updated and enlarged with new sections deepening the knowledge about data analysis. Moreover, a customized set of problems with solutions is accessible on the Web at extras.springer.com.Trade ReviewFrom the book reviews:“The book is carefully divided into two parts. The first part deals with modeling of statistical systems. The second part is devoted to the analysis of the respective systems. … followed by a section that offers helpful hints and solutions to problems throughout the text, making it easier for students to deepen their understanding and confidence in their newfound knowledge. … topics in each chapter are carefully selected and are well presented, making it a reliable reference for ‘statistical physics.’” (Technometrics, Vol. 55 (2), May, 2013)Table of ContentsStatistical Physics is more than Statistical Mechanics.- Part I: Modeling of Statistical Systems.- Random Variables: Fundamentals of Probability Theory and Statistics.- Random Variables in State Space: Classical Statistical Mechanics of Fluids.- Random Fields: Textures and Classical Statistical Mechanics of Spin Systems.- Time-Dependent Random Variables: Classical Stochastic Processes.- Quantum Random Systems.- Changes of External Conditions.- Part II: Analysis of Statistical Systems.- Estimation of Parameters.- Signal Analysis: Estimation of Spectra.- Estimators Based on a Probability Distribution for the Parameters.- Identification of Stochastic Models from Observations.- Estimating the Parameters of a Hidden Stochastic Model.- Statistical Tests and Classification Methods.- Appendix: Random Number Generation for Simulating Realizations of Random Variables.- Problems.- Hints and Solutions.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Limits of Predictability
Book SynopsisOne of the driving forces behind much of modern science and technology is the desire to foresee and thereby control the future. In recent years, however, it has become clear that, even in a deterministic world, there is alimit to the accuracy with which we can predict the future. This book details, in a largely nontechnical style, the extent to which we can predict the future development of various physical, biological and socio-economic processes.Table of Contents1. Introduction.- References.- 2. Forecasting Weather and Climate.- 2.1 Weather and Climate.- 2.2 Dynamical Systems and Their Properties.- 2.3 Weather Predictability.- 2.4 Elements of Stationary Random Process Prediction Theory.- 2.5 Predictability of Climatic Processes.- 2.6 Ways to Improve Statistical Forecasting.- 2.7 Utilization of Forecasting Results.- 2.8 Conclusion.- References.- 3. How an Active Autowave Medium Can Be Used to Predict the Future.- 3.1 Prediction.- 3.2 Active Autowave Media.- 3.3 Autowave Propagation in Energy-Restoring Active Media.- 3.4 Dynamics of Autowave Interaction.- 3.5 The External Medium Model and Its Fourier Image.- 3.6 Non-isochronism of Cyclic Processes.- 3.7 Harmonious Modulation and Modulation of Harmonics.- 3.8 The Fourier Image Cleared by the Active Autowave Medium.- References.- 4. Synergetics, Predictability and Deterministic Chaos.- 4.1 Dynamical Chaos.- 4.2 Nonlinearity and Open Systems Behavior.- 4.3 Synergetics and Order Parameters.- 4.4 Strangeness of the Strange Attractors.- 4.5 Dynamical Chaos and Reality.- 4.6 Dynamical Chaos. Gates of Fairyland.- References.- 5. The Information-Theoretic Approach to Assessing Reliability of Forecasts.- 5.1 Assessing Forecasts.- 5.2 Forecasting as the Subject Matter of Information Theory.- 5.3 An Example.- 5.4 Optimization of Forecasting Methods.- 5.5 Properties Shared by Prediction Methods.- 5.6 The Connection Between Discounting and Non-stationarity.- 5.7 Conclusion.- References.- 6. Prediction of Time Series.- 6.1 The Problem.- 6.2 Genesis of Random Phenomena.- 6.3 Time Series Prediction Based on Dynamical Chaos Theory.- 6.4 Prediction of Point Processes.- 6.5 The Nature of Errors Hindering Prediction.- 6.6 Prediction of Strong Earthquakes.- References.- 7. Fundamental and Practical Limits of Predictability.- 7.1 Predictability.- 7.2 Real, Observed, and Model Processes.- 7.3 Degree of Predictability. The Predictability Horizon.- 7.4 Searching for Prediction Models.- 7.5 Limits to Predictability.- 7.6 Dynamical Analogs to Social and Economic Phenomena.- 7.7 Conclusion.- References.- 8. The Future is Foreseeable but not Predictable: The ‘Oedipus Effect’ in Social Forecasting.- 8.1 Historical Background.- 8.2 The ‘Oedipus Effect’ in Social Forecasting.- 8.3 The Problem of Foresight and Prediction in Globalistics.- 8.4 The Problem of Foreseeing and Predicting the Development of the Former Soviet Society.- References.- Appendix A: Looking Back on the August 1991 Coup.- Appendix B: Looking Ahead.- 9. The Self-Organization of American Society in Presidential and Senatorial Elections.- 9.1 Historical Background.- 9.2 The American Presidential Election: Formal Analysis.- 9.3 Midterm Senatorial Elections: Formal Analysis.- 9.4 Discussion.- References.- 10. Problems of Predictability in Ethnogenic Studies.- References.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Principles of Advanced Mathematical Physics: Volume II
Table of Contents18 Elementary Group Theory.- 18.1 The group axioms; examples.- 18.2 Elementary consequences of the axioms; further definitions.- 18.3 Isomorphism.- 18.4 Permutation groups.- 18.5 Homomorphisms; normal subgroups.- 18.6 Cosets.- 18.7 Factor groups.- 18.8 The Law of Homomorphism.- 18.9 The structure of cyclic groups.- 18.10 Translations, inner automorphisms.- 18.11 The subgroups of ?4.- 18.12 Generators and relations; free groups.- 18.13 Multiply periodic functions and crystals.- 18.14 The space and point groups.- 18.15 Direct and semidirect products of groups; symmorphic space groups.- 19 Continuous Groups.- 19.1 Orthogonal and rotation groups.- 19.2 The rotation group SO(3); Euler’s theorem.- 19.3 Unitary groups.- 19.4 The Lorentz groups.- 19.5 Group manifolds.- 19.6 Intrinsic coordinates in the manifold of the rotation group.- 19.7 The homomorphism of SU(2) onto SO(3).- 19.8 The homomorphism of SL(2, ?) onto the proper Lorentz group ? p.- 19.9 Simplicity of the rotation and Lorentz groups.- 20 Group Representations I: Rotations and Spherical Harmonics.- 20.1 Finite-dimensional representations of a group.- 20.2 Vector and tensor transformation laws.- 20.3 Other group representations in physics.- 20.4 Infinite-dimensional representations.- 20.5 A simple case: SO(2).- 20.6 Representations of matrix groups on X?.- 20.7 Homogeneous spaces.- 20.8 Regular representations.- 20.9 Representations of the rotation group SO(3).- 20.10 Tesseral harmonics; Legendre functions.- 20.11 Associated Legendre functions.- 20.12 Matrices of the irreducible representations of SO(3); the Euler angles.- 20.13 The addition theorem for tesseral harmonics.- 20.14 Completeness of the tesseral harmonics.- 21 Group Representations II: General; Rigid Motions; Bessel Functions.- 21.1 Equivalence; unitary representations.- 21.2 The reduction of representations.- 21.3 Schur’s Lemma and its corollaries.- 21.4 Compact and noncompact groups.- 21.5 Invariant integration; Haar measure.- 21.6 Complete system of representations of a compact group.- 21.7 Homogeneous spaces as configuration spaces in physics.- 21.8 M2 and related groups.- 21.9 Representations of M2.- 21.10 Some irreducible representations.- 21.11 Bessel functions.- 21.12 Matrices of the representations.- 21.13 Characters.- 22 Group Representations and Quantum Mechanics.- 22.1 Representations in quantum mechanics.- 22.2 Rotations of the axes.- 22.3 Ray representations.- 22.4 A finite-dimensional case.- 22.5 Local representations.- 22.6 Origin of the two-valued representations.- 22.7 Representations of SU(2) and SL(2, ?).- 22.8 Irreducible representations of SU(2).- 22.9 The characters of SU(2).- 22.10 Functions of z and z?.- 22.11 The finite-dimensional representations of SL(2, ?).- 22.12 The irreducible invariant subspaces of X? for SL(2, ?).- 22.13 Spinors.- 23 Elementary Theory of Manifolds.- 23.1 Examples of manifolds; method of identification.- 23.2 Coordinate systems or charts; compatibility; smoothness.- 23.3 Induced topology.- 23.4 Definition of manifold; Hausdorff separation axiom.- 23.5 Curves and functions in a manifold.- 23.6 Connectedness; components of a manifold.- 23.7 Global topology; homotopic curves; fundamental group.- 23.8 Mechanical linkages: Cartesian products.- 24 Covering Manifolds.- 24.1 Definition and examples.- 24.2 Principles of lifting.- 24.3 Universal covering manifold.- 24.4 Comments on the construction of mathematical models.- 24.5 Construction of the universal covering.- 24.6 Manifolds covered by a given manifold.- 25 Lie Groups.- 25.1 Definitions and statement of objectives.- 25.2 The expansions of m(·, ·) and l(·, ·).- 25.3 The Lie algebra of a Lie group.- 25.4 Abstract Lie algebras.- 25.5 The Lie algebras of linear groups.- 25.6 The exponential mapping; logarithmic coordinates.- 25.7 An auxiliary lemma on inner automorphisms; the mappings Ad?.- 25.8 Auxiliary lemmas on formal derivatives.- 25.9 An auxiliary lemma on the differentiation of exponentials.- 25.10 The Campbell-Baker-Hausdorf (CBH) formula.- 25.11 Translation of charts; compatibility; G as an analytic manifold.- 25.12 Lie algebra homomorphisms.- 25.13 Lie group homomorphisms.- 25.14 Law of homomorphism for Lie groups.- 25.15 Direct and semidirect sums of Lie algebras.- 25.16 Classification of the simple complex Lie algebras.- 25.17 Models of the simple complex Lie algebras.- 25.18 Note on Lie groups and Lie algebras in physics.- Appendix to Chapter 25—Two nonlinear Lie groups.- 26 Metric and Geodesics on a Manifold.- 26.1 Scalar and vector fields on a manifold.- 26.2 Tensor fields.- 26.3 Metric in Euclidean space.- 26.4 Riemannian and pseudo-Riemannian manifolds.- 26.5 Raising and lowering of indices.- 26.6 Geodesies in a Riemannian manifold.- 26.7 Geodesies in a pseudo-Riamannian manifold M.- 26.8 Geodesies; the initial-value problem; the Lipschitz condition.- 26.9 The integral equation; Picard iterations.- 26.10 Geodesies; the two-point problem.- 26.11 Continuation of geodesies.- 26.12 Affmely connected manifolds.- 26.13 Riemannian and pseudo-Riemannian covering manifolds.- 27 Riemannian, Pseudo-Riemannian, and Affinely Connected Manifolds.- 27.1 Topology and metric.- 27.2 Geodesic or Riemannian coordinates.- 27.3 Normal coordinates in Riemannian and pseudo-Riemannian manifolds.- 27.4 Geometric concepts; principle of equivalence.- 27.5 Covariant differentiation.- 27.6 Absolute differentiation along a curve.- 27.7 Parallel transport.- 27.8 Orientability.- 27.9 The Riemann tensor, general; Laplacian and d’Alembertian.- 27.10 The Riemann tensor in a Riemannian or pseudo-Riemannian manifold.- 27.11 The Riemann tensor and the intrinsic curvature of a manifold.- 27.12 Flatness and the vanishing of the Riemann tensor.- 27.13 Eisenhart’s analysis of the Stäckel systems.- 28 The Extension of Einstein Manifolds.- 28.1 Special relativity.- 28.2 The Einstein gravitational field equations.- 28.3 The Schwarzschild charts.- 28.4 The Finkelstein extensions of the Schwarzschild charts.- 28.5 The Kruskal extension.- 28.6 Maximal extensions; geodesic completeness.- 28.7 Other extensions of the Schwarzschild manifolds.- 28.8 The Kerr manifolds.- 28.9 The Cauchy problem.- 28.10 Concluding remarks.- 29 Bifurcations in Hydrodynamic Stability Problems.- 29.1 The classical problems of hydrodynamic stability.- 29.2 Examples of bifurcations in hydrodynamics.- 29.3 The Navier-Stokes equations.- 29.4 Hilbert space formulation.- 29.5 The initial-value problem; the semiflow in ?.- 29.6 The normal modes.- 29.7 Reduction to a finite-dimensional dynamical system.- 29.8 Bifurcation to a new steady state.- 29.9 Bifurcation to a periodic orbit.- 29.10 Bifurcation from a periodic orbit to an invariant torus.- 29.11 Subharmonic bifurcation.- Appendix to Chapter 29—Computational details for the invariant torus.- 30 Invariant Manifolds in the Taylor Problem.- 30.1 Survey of the Taylor problem to 1968.- 30.2 Calculation of invariant manifolds.- 30.3 Cylindrical coordinates.- 30.4 The Hilbert space.- 30.5 Separation of variables in cylindrical coordinates.- 30.6 Results to date for the Taylor problem.- Appendix to Chapter 30—The matrices in Eagles’ formulation.- 31 The Early Onset of Turbulence.- 31.1 The Landau-Hopf model.- 31.2 The Hopf example.- 31.3 The Ruelle-Takens model.- 31.4 The co-limit set of a motion.- 31.5 Attractors.- 31.6 The power spectrum for motions in ?n.- 31.7 Almost periodic and aperiodic motions.- 31.8 Lyapounov stability.- 31.9 The Lorenz system; the bifurcations.- 31.10 The Lorenz attractor; general description.- 31.11 The Lorenz attractor; aperiodic motions.- 31.12 Statistics of the mapping f and g.- 31.13 The Lorenz attractor; detailed structure I.- 31.14 The symbols [i, j] of Williams.- 31.15 Prehistories.- 31.16 The Lorenz attractor; detailed structure II.- 31.17 Existence of 1-cells in F.- 31.18 Bifurcation to a strange attractor.- 31.19 The Feigenbaum model.- Appendix to Chapter 31 (Parts A-H)—Generic properties of systems:.- 31.A Spaces of systems.- 31.B Absence of Lebesgue measure in a Hilbert space.- 31.C Generic properties of systems.- 31.D Strongly generic; physical interpretation.- 31.E Peixoto’s theorem.- 31.F Other examples of generic and nongeneric properties.- 31.G Lack of correspondence between genericity and Lebesgue measure 308 31.H Probability and physics.- References.
£40.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Scattering Amplitudes in Gauge Theories
Book SynopsisAt the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge.These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory.Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications.The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.Trade Review“Aimed at the advanced graduate student or a practitioner of high energy theory interested in the subject, the book begins with a review of non-abelian gauge theory and its conventional Feynman methods before immediately delving into on-shell recursion relations of BCFW (Britto-Cachazo-Feng-Witten) and factorization properties. … Of particular usefulness to the student are the exercises and an entire appendix dedicated to their detailed solutions.” (Yang-Hui He, zbMATH 1315.81005, 2015)Table of ContentsIntroduction and Basics.- Tree-Level Techniques.- Loop-Level Structure.- Advanced Topics.- Renormalization Properties of Wilson Loops.- Conventions and Useful Formulae.- Solutions to the Exercises.- References.
£24.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Large Deviations in Physics: The Legacy of the Law of Large Numbers
Book SynopsisThis book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.Table of ContentsErgodicity – A Basic Concept.- Large Deviations in Statistical Mechanics: Rigorous and Non-Rigorous.- Large Deviation Techniques for Long-Range Interactions.- Fluctuation-Dissipation and Fluctuation Relations: From Equilibrium to Nonequilibrium Phenomena and Back.- Stochastic Fluctuations in Deterministic Systems.- Large Deviation and Disordered Systems.- Large Deviations in Turbulence.- Ergodicity Breaking Challenges Monte Carlo Methods.- Anomalous Diffusion: Deterministic and Stochastic Perspectives.- The Use of Fluctuation Relations for the Analysis of Free-Energy Landscapes.
£61.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Clifford Algebras and Lie Theory
Book SynopsisThis monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem.This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra.Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.Table of ContentsPreface.- Conventions.- List of Symbols.- 1 Symmetric bilinear forms.- 2 Clifford algebras.- 3 The spin representation.- 4 Covariant and contravariant spinors.- 5 Enveloping algebras.- 6 Weil algebras.- 7 Quantum Weil algebras.- 8 Applications to reductive Lie algebras.- 9 D(g; k) as a geometric Dirac operator.- 10 The Hopf–Koszul–Samelson Theorem.- 11 The Clifford algebra of a reductive Lie algebra.- A Graded and filtered super spaces.- B Reductive Lie algebras.- C Background on Lie groups.- References.- Index.
£113.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Group Theory and Quantum Mechanics
Book SynopsisThe German edition of this book appeared in 1932 under the title "Die gruppentheoretische Methode in der Quantenmechanik". Its aim was, to explain the fundamental notions of the Theory of Groups and their Representations, and the application of this theory to the Quantum Mechanics of Atoms and Molecules. The book was mainly written for the benefit of physicists who were supposed to be familiar with Quantum Mechanics. However, it turned out that it was also used by. mathematicians who wanted to learn Quantum Mechanics from it. Naturally, the physical parts were too difficult for mathematicians, whereas the mathematical parts were sometimes too difficult for physicists. The German language created an additional difficulty for many readers. In order to make the book more readable for physicists and mathe maticians alike, I have rewritten the whole volume. The changes are most notable in Chapters 1 and 6. In Chapter t, I have tried to give a mathematically rigorous exposition of the principles of Quantum Mechanics. This was possible because recent investigations in the theory of self-adjoint linear operators have made the mathematical foundation of Quantum Mechanics much clearer than it was in t 932. Chapter 6, on Molecule Spectra, was too much condensed in the German edition. I hope it is now easier to understand. In Chapter 2-5 too, numerous changes were made in order to make the book more readable and more useful.Table of Contents1. Fundamental Notions of Quantum Mechanics.- § 1. Wave Functions.- § 2. Hilbert Spaces.- § 3. Linear Operators.- § 4. Hypermaximal Operators.- § 5. Separation of Variables.- § 6. One Electron in a Central Field.- § 7. Perturbation Theory.- § 8. Angular Momentum and Infinitesimal Rotations.- 2. Groups and Their Representations.- § 9. Linear Transformations.- § 10. Groups.- § 11. Equivalence and Reducibility of Representations.- § 12. Representations of Abelian Groups. Examples.- § 13. Uniqueness Theorems.- § 14. Kronecker’s Product Transformation.- § 15. The Operators Commuting with all Operators of a Given Representation.- § 16. Representations of Finite Groups.- § 17. Group Characters.- 3. Translations, Rotations and Lorentz Transformations.- § 18. Lie Groups and their Infinitesimal Transformations.- A. Lie Groups.- B. One-dimensional Lie Groups and Semi-Groups.- C. Causality and Translations in Time.- D. The Lie Algebra of a Lie Group.- E. Representations of Lie Groups.- § 19. The Unitary Groups SU(2) and the Rotation Group O3.- § 20. Representations of the Rotation Group O3.- § 21. Examples and Applications.- A. The Product Representation ?j × ?j’.- B. The Clebsch-Gordan Series.- C. Applications of (21.1).- D. The Reflection Character.- § 22. Selection and Intensity Rules.- § 23. The Representations of the Lorentz Group.- A. The Group SL(2) and the Restricted Lorentz Group.- B. Infinitesimal Transformations.- C. The Relation between World Vectors and Spinors.- IV. The Spinning Electron.- § 24. The Spin.- § 25. The Wave Function of the Spinning Electron.- A. Pauli’s Pair of Functions (?1, ?2).- B. Transformation of the Pair (?1, ?2).- C. Infinitesimal Rotations.- D. The Angular Momenta.- E. The Doublet Splitting of the Alkali Terms.- G. The Inversion s.- § 26. Dirac’s Wave Equation.- § 27. Two-Component Spinors.- A. Dirac’s Equation Rewritten.- B. Weyl’s Equation.- § 28. The Several Electron Problem. Multiplet Structure. Zeeman Effect.- V. The Group of Permutations and the Exclusion Principle.- § 29. The Resonance of Equal Particles.- § 30. The Exclusion Principle and the Periodical System.- § 31. The Eigenfunctions of the Atom.- § 32. The Calculation of the Energy Values.- § 33. Pure Spin Functions and their Transformation under Rotations and Permutations.- § 34. Representations of the Symmetric Group Sn.- VI. Molecule Spectra.- § 35. The Quantum Numbers of the Molecule.- § 36. The Rotation Levels.- § 37. The Case of Two Equal Nuclei.- Author and Subject Index.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Implementation of Finite Element Methods for Navier-Stokes Equations
Book SynopsisIn structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.Table of ContentsNotations.- 1. Elliptic Equations of Order 2: Some Standard Finite Element Methods.- 1.1. A 1-Dimensional Model Problem: The Basic Notions.- 1.2. A 2-Dimensional Problem.- 1.3. The Finite Element Equations.- 1.4. Standard Examples of Finite Element Methods.- 1.4.1. Example 1: The P1-Triangle (Courant’s Triangle).- 1.4.2. Example 2: The P2-Triangle.- 1.4.3. Example 3: The Q1-Quadrangle.- 1.4.4. Example 4: The Q2-Quadrangle.- 1.4.5. A Variational Crime: The P1 Nonconforming Element.- 1.5. Mixed Formulation and Mixed Finite Element Methods for Elliptic Equations.- 1.5.1. The One Dimensional Problem.- 1.5.2. A Two Dimensional Problem.- 2. Upwind Finite Element Schemes.- 2.1. Upwind Finite Differences.- 2.2. Modified Weighted Residual (MWR).- 2.3. Reduced Integration of the Advection Term.- 2.4. Computation of Directional Derivatives at the Nodes.- 2.5. Discontinuous Finite Elements and Mixed Interpolation.- 2.6. The Method of Characteristics in Finite Elements.- 2.7. Peturbation of the Advective Term: Bredif (1980).- 2.8. Some Numerical Tests and Further Comments.- 2.8.1. One Dimensional Stationary Advection Equation (56).- 2.8.2. Two Dimensional Stationary Advection Equation.- 2.8.3. Time Dependent Advection.- 3. Numerical Solution of Stokes Equations.- 3.1. Introduction.- 3.2. Velocity—Pressure Formulations: Discontinuous Approximations of the Pressure.- 3.2.1. uh: P1 Nonconforming Triangle (§1-4-5); ph: Piecewise Constant.- 3.2.2. uh: P2 Triangle ph: P0 (Piecewise Constant).- 3.2.3. uh: “P2+bubble” Triangle (or Modified P2); ph: Discontinuous P1.- 3.2.4. uh: Q2 Quadrangle; ph: Q1 Discontinuous.- 3.2.5. Numerical Solution by Penalty Methods.- 3.2.6. Numerical Results and Further Comments.- 3.3. Velocity—Pressure Formulations: Continuous Approximation of the Pressure and Velocity.- 3.3.1. Introduction.- 3.3.2. Examples and Error Estimates.- 3.3.3. Decomposition of the Stokes Problem.- 3.4. Vorticity—Pressure—Velocity Formulations: Discontinuous Approximations of Pressure and Velocity.- 3.5. Vorticity Stream-Function Formulation: Decompositions of the Biharmonic Problem.- 4. Navier-Stokes Equations: Accuracy Assessments and Numerical Results.- 4.1. Remarks on the Formulation.- 4.2. A review of the Different Methods.- 4.2.1 Velocity—Pressure Formulations: Discontinuous Approximations of the Pressure.- 4.2.2. Velocity—Pressure Formulations: Continuous Approximations of the Pressure.- 4.2.3. Vorticity—Pressure—Velocity Formulations: Discontinuous Approximations of Pressure and Velocity.- 4.2.4. Vorticity Stream-Function Formulation.- 4.3. Some Numerical Tests.- 4.3.1. The Square Wall Driven Cavity Flow.- 4.3.2. An Engineering Problem: Unsteady 2-D Flow Around and In an Air-Intake.- 5. Computational Problems and Bookkeeping.- 5.1. Mesh Generation.- 5.2. Solution of the Nonlinear Problems.- 5.2.1. Successive Approximations (or Linearization) with Under Relaxation.- 5.2.2. Newton-Raphson Algorithm.- 5.2.3. Conjugate Gradient Method (with Scaling) for Nonlinear Problems.- 5.2.4. A Splitting Technique for the Transient Problem.- 5.3. Iterative and Direct Solvers of Linear Equations.- 5.3.1. Successive Over Relaxation.- 5.3.2. Cholesky Factorizations.- 5.3.3. Out of Core Factorizations.- 5.3.4. Preconditioned Conjugate Gradient.- Appendix 2. Numerical Illustration.- Three Dimensional Case.- References.
£42.74
Springer Fachmedien Wiesbaden Ausgewählte Kapitel der Höheren Mathematik:
Book SynopsisAnimationen im Internet veranschaulichen z. B. die Wellengleichung durch eine schwingende Membran, die Wärmeleitung durch eine abnehmende Temperaturverteilung und die Potentialgleichung durch ein von der Randbelegung aufgeprägtes Potenzial. Welche Methoden verbergen sich dahinter, wie erzeugt man diese Animationen? Darauf soll der Leser eine erschöpfende Antwort geben können. Auf ausführliche, formale Beweise wird verzichtet. Die Begriffe werden mittels Beispielen und Graphiken in ihren Grundideen veranschaulicht und motiviert. Der Leser soll Hintergrundwissen und Lösungskompetenz bekommen, damit er sich nicht mit der Formelmanipulation zufrieden geben muss. Studierende sollen in die Lage versetzt werden, Probleme, die sich aus ihrer Bachelor/Masterarbeit oder aus den Anwendungen ergeben, zu bearbeiten. Table of ContentsTensoren.- Tensorfelder.- Kurven- und Flächenintegrale.- Orthogonale Systeme von Polynomen.- Lineare Differentialgleichungen im Komplexen.- Stabilität dynamischer Systeme.- Partielle Differentialgleichungen.- Gleichungen erster Ordnung.- Gleichungen zweiter Ordnung.- Wellengleichung.- Wärmeleitungsgleichung.- Potentialgleichung.
£26.59
Springer Fachmedien Wiesbaden Theorie und Numerik elliptischer
Book SynopsisDas Verständnis der numerischen Behandlung elliptischer Differentialgleichungen erfordert notwendigerweise auch die Kenntnisse der Theorie der Differentialgleichungen. Deshalb behandelt das Buch beide parallel. Zunächst wird der klassische Zugang (starke Lösungen, Differenzenverfahren) beschrieben. Dem Maximum-Minimum-Prinzip auf der theoretischen Seite entsprechen beispielsweise die Eigenschaften der M-Matrizen, die sich bei der Diskretisierung ergeben. Nach einem Exkurs über die Funktionalanalysis werden die Variationsformulierung und die Finite-Element-Diskretisierungen behandelt. Weitere Themen sind die Analyse der Diskretisierungen von Eigenwertaufgaben und die Stokes-Gleichungen mit den inf-sup-Bedingungen für die Finite-Element-Diskretisierung. Auf der theoretischen Seite wird die Regularität der Lösungen näher untersucht.Gegenüber der zweiten Auflage enthält der vorliegende Text zahlreiche Aktualisierungen, vor allem im Bereich der Finiten Elemente sowie in den Literaturangaben. Außerdem wurden die vollständigen Lösungen der Übungsaufgaben hinzugefügt.Table of ContentsPartielle Differentialgleichungen und ihre Typeneinteilung.- Die Potentialgleichung.- Die Poisson-Gleichung .- Differenzenmethode für die Poisson-Gleichung.- Allgemeine Randwertaufgaben.- Exkurs über Funktionalanalysis.- Variationsformulierung.- Die Methode der finiten Elemente.- Regularität.- Spezielle Differentialgleichungen.- Eigenwertprobleme elliptischer Operatoren.- Stokes-Gleichungen.- Lösungen der Übungsaufgaben.
£23.74
Springer Spektrum Schnellstart Python: Ein Einstieg Ins
Book Synopsis
£9.99
Springer Fachmedien Wiesbaden Quantenmechanik: Einführung in die mathematische
Book SynopsisWer schon immer die Hieroglyphen auf Sheldons Tafel in der Fernsehserie The Big Bang Theory verstehen oder ganz genau wissen wollte, was es mit dem Schicksal von Schrödingers Katze auf sich hat, findet in diesem essential eine kurze, anschauliche Einführung in die Welt der Quantenmechanik. Speziell fokussiert sich der Text auf die mathematische Beschreibung im Hilbertraum. Hierbei geht der Inhalt über populärwissenschaftliche Darstellungen hinaus, ist allerdings trotzdem durch die anschaulichen Beispiele für Lesende ohne spezielle Vorkenntnisse geeignet. Der Autor:Prof. Dr. Martin Pieper ist seit 2011 Professor für Mathematik und Simulation an der FH Aachen. Vor seinem Ruf an die FH Aachen war er wissenschaftlicher Mitarbeiter in der Abteilung Optimierung des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik. Table of ContentsQuantenmechanik in Hilberträumen.- Postulate der Quantenmechanik.- Diskrete Energieniveaus mit Entartung.- Teilchen im Potentialkasten, Stern-Gerlach-Versuch und Schrödingers Katze.
£9.99
Springer Spektrum Thermodynamische Potenziale Und Zustandssumme:
Book Synopsis
£9.99
Springer Spektrum Die Eigenschaften Der Stoffe: Suszeptibilitäten
Book Synopsis
£9.99
Springer Spektrum Das Zwillingsparadoxon
Book Synopsis
£9.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Astronomy on the Personal Computer
Book SynopsisA thorough introduction to the computation of celestial mechanics, covering everything from astronomical and computational theory to the construction of rapid and accurate applications programs. The book supplies the necessary knowledge and software solutions for determining and predicting positions of the Sun, Moon, planets, minor planets and comets, solar eclipses, stellar occultations by the Moon, phases of the Moon and much more. This completely revised edition takes advantage of C++, and individual applications may be efficiently realized through the use of a powerful module library. The accompanying CD-ROM contains the complete, fully documented and commented source codes as well as executable programs for Windows 98/2000/XP and LINUX.Table of Contents1 Introduction.- 2 Coordinate Systems.- 3 Calculation of Rising and Setting Times.- 4 Cometary Orbits.- 5 Special Perturbations.- 6 Planetary Orbits.- 7 Physical Ephemerides of the Planets.- 8 The Orbit of the Moon.- 9 Solar Eclipses.- 10 Stellar Occultations.- 11 Orbit Determination.- 12 Astrometry.- A.1 The Accompanying CD-ROM.- A.1.1 Contents.- A.1.2 System Requirements.- A.1.3 Executing the Programs.- A.2 Compiling and Linking the Programs.- A.2.1 General Advice on Computer-Specific Modifications.- A.2.2 Microsoft Visual C++ for Windows 98/2000/XP.- A.2.3 GNU C++ for Linux.- A.3 List of the Library Functions.- Symbols.
£94.99
