Mathematical / Computational / Theoretical physics Books
Birkhauser Verlag AG Ground state properties and excitation spectrum
Book SynopsisElectron gas theory is one of the broadest fields in theoretical condensed matter physics, and even its most elementary application to the study of collective excitations and screening in the simpe metals poses interesting questions. Recent Electron Energy Loss and Inelastic X-Ray Scattering experiments have shown that traditional electron gas theories are unable to account for the measured plasmon dispersion relation. While it has become clear that neither correlation nor band structure alone can explain those results, the recently developed Time Dependent Density Functional Theory provides a general framework which can account for both.
£14.16
Birkhauser Verlag AG Quantum Gases in Quasi-One-Dimensional Arrays
Book SynopsisThe experimental achievement of Bose-Einstein condensation (1995) and of Fermi degeneracy (1999) in ultra-cold, dilute gases has opened a new field in atomic physics and condensed matter physics. This thesis presents an overview of theoretical and experimental facts on ultra-cold atomic gases. A Green's function scheme is examined, and the book also applies a novel spin-density-functional approach to the study of Fermi gases inside one-dimensional optical lattices.Table of ContentsPreface.- 1. Reviews on Ultra-cold quantum gases.- 2. Theory of matter transport in quasi-1D arrays.- 3. Density-functional theory of 1D Fermi gases.- 4. Ultra-cold attractive fermions in 1D optical lattices.
£14.24
Birkhauser Verlag AG Asymptotics in Dynamics, Geometry and PDEs;
Book SynopsisThese are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with: mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, local dynamics: parabolic systems, small denominator questions, new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, a new family of resurgent functions related to knot theory.
£25.64
Birkhauser Verlag AG Resurgence, Physics and Numbers
Book SynopsisThis book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematica Ennio de Giorgi in Pisa, on May 18-22, 2015. This meeting originally stemmed from the impressive upsurge of interest for Jean Ecalle's alien calculus in Physics, in the last years – a trend that has considerably developed since then. The volume contains both original research papers and surveys, by leading experts in the field, reflecting the themes that were tackled at this event: Stokes phenomenon and resurgence, in various mathematical and physical contexts but also related constructions in algebraic combinatorics and results concerning numbers, specifically multiple zetavalues. Table of ContentsAsymptotics, ambiguities and resurgence.- Nonlinear eigenvalue problems.- Feynman diagrams and their algebraic lattices.- Invariants of identity-tangent diffeomorphisms expanded as series of multitangents and multizetas.- The resurgent approach to topological string theory.- WKB and resurgence in the Mathieu equation.- Renormalised conical zeta values.- Combinatorics of Poincaré's and Schröder's equations.
£21.84
Birkhauser Verlag AG Symmetry Breaking in the Standard Model: A
Book SynopsisThe book provides a non-perturbative approach to the symmetry breaking in the standard model, in this way avoiding the critical issues which affect the standard presentations. The debated empirical meaning of global and local gauge symmetries is clarified. The absence of Goldstone bosons in the Higgs mechanism is non-perturbatively explained by the validity of Gauss laws obeyed by the currents which generate the relatedglobal gauge symmetry. The solution of the U(1) problem and the vacuum structure in quantum chromodynamics (QCD) are obtained without recourse to the problematic semiclassical instanton approximation, by rather exploiting the topology of the gauge group.Table of ContentsSpontaneous symmetry breaking.- Goldstone theorem. Breaking gauge symmetries.- Higgs mechanism.- U(1) problem in QCD; a solution without instantons.- Gauge group topology and $\theta$ vacuum structure.
£17.09
Springer Low Reynolds number hydrodynamics: with special applications to particulate media
Book SynopsisOne studying the motion of fluids relative to particulate systems is soon impressed by the dichotomy which exists between books covering theoretical and practical aspects. Classical hydrodynamics is largely concerned with perfect fluids which unfortunately exert no forces on the particles past which they move. Practical approaches to subjects like fluidization, sedimentation, and flow through porous media abound in much useful but uncorrelated empirical information. The present book represents an attempt to bridge this gap by providing at least the beginnings of a rational approach to fluid particle dynamics, based on first principles. From the pedagogic viewpoint it seems worthwhile to show that the Navier-Stokes equations, which form the basis of all systematic texts, can be employed for useful practical applications beyond the elementary problems of laminar flow in pipes and Stokes law for the motion of a single particle. Although a suspension may often be viewed as a continuum for practical purposes, it really consists of a discrete collection of particles immersed in an essentially continuous fluid. Consideration of the actual detailed boundary value problems posed by this viewpoint may serve to call attention to the limitation of idealizations which apply to the overall transport properties of a mixture of fluid and solid particles.Table of Contents1. Introduction.- 1–1 Definition and purpose, 1. 1–2 Historical review, 8. 1–3 Application in science and technology, 13..- 2. The Behavior of Fluids in Slow Motion.- 2–1 The equations of change for a viscous fluid, 23. 2–2 Mechanical energy dissipation in a viscous fluid, 29. 2–3 Force and couple acting on a body moving in a viscous fluid, 30. 2–4 Exact solutions of the equations of motion for a viscous fluid, 31. 2–5 Laminar flow in ducts, 33. 2–6 Simplifications of the Navier-Stokes equations, especially for slow motion, 40. 2–7 Paradoxes in the solution of the creeping motion equations, 47. 2–8 Molecular effects in fluid dynamics, 49. 2–9 Non-newtonian flow, 51. 2–10 Unsteady creeping flows, 52..- 3. Some General Solutions and Theorems Pertaining to the Creeping Motion Equations.- 3–1 Introduction, 58. 3–2 Spherical coordinates, 62. 3–3 Cylindrical coordinates, 71. 3–4 Integral representations, 79. 3–5 Generalized reciprocal theorem, 85. 3–6 Energy dissipation, 88..- 4. Axisymmetrical Flow.- 4–1 Introduction, 96. 4–2 Stream function, 96. 4–3 Relation between stream function and local velocity, 98. 4–4 Stream function in various coordinate systems, 99. 4–5 Intrinsic coordinates, 100. 4–6 Properties of the stream function, 102. 4–7 Dynamic equation satisfied by the stream function, 103. 4–8 Uniform flow, 106. 4–9 Point source or sink, 106. 4–10 Source and sink of equal strength, 107. 4–11 Finite line source, 108. 4–12 Point force, 110. 4–13 Boundary conditions satisfied by the stream function, 111. 4–14 Drag on a body, 113. 4–15 Pressure, 116. 4–16 Separable coordinate systems, 117. 4–17 Translation of a sphere, 119. 4–18 Flow past a sphere, 123. 4–19 Terminal settling velocity, 124. 4–20 Slip at the surface of a sphere, 125. 4–21 Fluid sphere, 127. 4–22 Concentric spheres, 130. 4–23 General solution in spherical coordinates, 133. 4–24 Flow through a conical diffuser, 138. 4–25 Flow past an approximate sphere, 141. 4–26 Oblate spheroid, 145. 4–27 Circular disk, 149. 4–28 Flow in a venturi tube, 150. 4–29 Flow through a circular aperture, 153. 4–30 Prolate spheroid, 154. 4–31 Elongated rod, 156. 4–32 Axisymmetric flow past a spherical cap, 157..- 5. The Motion of a Rigid Particle of Arbitrary Shape in an Unbounded Fluid.- 5–1. Introduction, 159. 5–2 Translational motions, 163. 5–3 Rotational motions, 169. 5–4 Combined translation and rotation, 173. 5–5 Symmetrical particles, 183. 5–6 Nonskew bodies, 192. 5–7 Terminal settling velocity of an arbitrary particle, 197. 5–8 Average resistance to translation, 205. 5–9 The resistance of a slightly deformed sphere, 207. 5–10 The settling of spherically isotropic bodies, 219. 5–11 The settling of orthotopic bodies, 220..- 6. Interaction between Two or More Particles.- 6–1 Introduction, 235. 6–2 Two widely spaced spherically isotropic particles, 240: 6–3 Two spheres by the method of reflections and similar techniques, 249. 6–4 Exact solution for two spheres falling along their line of centers, 270. 6–5 Comparison of theories with experimental data for two spheres, 273. 6–6 More than two spheres, 276. 6–7 Two spheroids in a viscous liquid, 278. 6–8 Limitations of creeping motion equations, 281..- 7. Wall Effects on the Motion of a Single Particle.- 7–1 Introduction, 286. 7–2 The translation of a particle in proximity to container walls, 288. 7–3 Sphere moving in an axial direction in a circular cylindrical tube, 298. 7–4 Sphere moving relative to plane walls, 322. 7–5 Spheroid moving relative to cylindrical and plane walls, 331. 7–6 k-coefficients for typical boundaries, 340. 7–7 One- and two-dimensional problems, 341. 7–8 Solid of revolution rotating symmetrically in a bounded fluid, 346. 7–9 Unsteady motion of a sphere in the presence of a plane wall, 354..- 8. Flow Relative to Assemblages of Particles.- 8–1 Introduction, 358. 8–2 Dilute systems—no interaction effects, 360. 8–3 Dilute systems—first-order interaction effects, 371. 8–4 Concentrated systems, 387. 8–5 Systems with complex geometry, 400. 8–6 Particulate suspensions, 410. 8–7 Packed beds, 417. 8–8 Fluidization, 422..- 9. The Viscosity of Particulate Systems.- 9–1 Introduction, 431. 9–2 Dilute systems of spheres—no interaction effects, 438. 9–3 Dilute systems—first-order interaction effects, 443. 9–4 Concentrated systems, 448. 9–5 Nonspherical and nonrigid particles, 456. 9–6 Comparison with data, 462. 9–7 Non-newtonian behavior, 469..- Appendix A. Orthogonal Curvilinear Coordinate Systems.- A-l Curvilinear coordinates, 474. A-2 Orthogonal curvilinear coordinates, 477. A-3 Geometrical properties, 480. A-4 Differentiation of unit vectors, 481. A-5 Vector differential invariants, 483. A-6 Relations between cartesian and orthogonal curvilinear coordinates, 486. A-7 Dyadics in orthogonal curvilinear coordinates, 488. A-8 Cylindrical coordinate systems, 490. A-9 Circular cylindrical coordinates, 490. A-10 Conjugate cylindrical coordinate systems, 494. A-ll Elliptic cylinder coordinates, 495. A-12 Bipolar cylinder coordinates, 497. A-l3 Parabolic cylinder coordinates, 500. A-14 Coordinate systems of revolution, 501. A-l5 Spherical Coordinates, 504. A-l6 Conjugate coordinate systems of revolution, 508. A-17 Prolate spheroidal coordinates, 509. A-18 Oblate spheroidal coordinates, 512. A-19 Bipolar coordinates, 516. A-20 Toroidal coordinates, 519. A-21 Paraboloidal Coordinates, 521..- Appendix B. Summary of Notation and Brief Review of Polyadic Algebra.- Name Index.
£123.49
Springer Selected Papers (1937 – 1976) of Julian Schwinger
Book SynopsisVery few people have contributed as much to twentieth-century physics as Julian Schwinger. It is therefore appropriate to offer a retrospective of his work on the occasion of his sixtieth birthday (February 12, 1978). We hope, in offering this selection of his papers, to bring to light ideas and results that may have been partly overlooked at the time of the original publication. Schwinger has published prodigiously on a great variety of subjects, as is evident from the comprehensive list of publications arranged in chronological order which appears on p. xiii. Needless to say, only a small subset could be included in the present modest volume. In the selection, great weight was assigned to papers that seem to be less widely known or appreciated than they deserve. Many important papers are therefore omitted. (Examples: Paper [64] 'On Gauge Invariance and Vacuum Polarization' and Paper [69] 'On Angular Momentum', both of which have been reprinted elsewhere. ) The collection is a personal one, having been chosen by Schwinger himself, and is therefore of particular interest. It would probably not be interesting to offer an analysis, by the editors, of Schwinger's contributions to physics. However, we are very pleased to be able to include Schwinger's own informal and very personal comments about each article that appears in this volume. These comments indicate his reasons for choosing these particular articles and, in many cases, provide a capsule synopsis of what he considers most valuable.Table of Contents[8] ‘The Scattering of Neutrons by Ortho- and Parahydrogen’ (with E. Teller), Phys. Rev.52, 286 (1937)..- [11] ‘The Neutron-Proton Scattering Cross Section’ (with V. Cohen and H. Goldsmith), Phys. Rev.55, 106 (1939)..- [15] ‘On Pair Emission in the Proton Bombardment of Fluorine’ (with J. R. Oppenheimer), Phys. Rev.56, 1066 (1939)..- [25] ‘On a Theory of Particles with Half-Integral Spin’ (with W. Rarita), Phys. Rev.60, 61 (1941)..- [26] ‘On the Interaction of Mesotrons and Nuclei’ (with J. R. Oppenheimer), Phys. Rev.60, 150 (1941)..- [31] ‘On a Field Theory of Nuclear Forces’, Phys. Rev.61, 387 (1942)..- [34] ‘Polarization of Neutrons by Resonance Scattering in Helium’, Phys. Rev.69, 681 (1946)..- [42] ‘On the Polarization of Fast Neutrons’, Phys. Rev.73, 407 (1948)..- [43] ‘On Quantum-Electrodynamics and the Magnetic Moment of the Electron’, Phys. Rev.73, 416 (1948)..- [44] ‘A Note on Saturation in Microwave Spectroscopy’ (with R. Karplus), Phys. Rev.73, 1020 (1948)..- [58] ‘On the Charge Independence of Nuclear Forces’, Phys. Rev.78, 135(1950)..- [66] ‘On the Green’s Functions of Quantized Fields I, II’, Proc. Natl. Acad. Sci., U.S.A.37, 452, 455 (1951)..- [74] ‘The Theory of Quantized Fields. III’, Phys. Rev.91, 728 (1953)..- [76] ‘The Theory of Quantized Fields. IV’, Phys. Rev.92, 1283 (1953)..- [78] ‘The Quantum Correction in the Radiation by Energetic Accelerated Electrons’, Proc. Natl. Acad. Sci., U.S.A.40, 132 (1954)..- [82] ‘A Theory of the Fundamental Interactions’, Ann. Phys. (N. Y.)2, 407 (1957)..- [86] ‘On the Euclidean Structure of Relativistic Field Theory’, Proc. Natl. Acad. Sci., U.S.A.44, 956 (1958)..- [88] ‘Euclidean Quantum Electrodynamics’, Phys. Rev.115, 721 (1959)..- [91] ‘The Algebra of Microscopic Measurement’, Proc. Natl. Acad. Sci., U.S.A.45, 1542 (1959)..- [98] ‘The Special Canonical Group’, Proc. Natl. Acad. Sci., U.S.A.46, 1401 (1960)..- [100] ‘On the Bound States of a Given Potential’, Proc. Natl. Acad. Sci., U.S.A.47, 122 (1961)..- [101] ‘Brownian Motion of a Quantum Oscillator’, J. Math. Phys.2, 407(1961)..- [104] ‘Gauge Invariance and Mass’, Phys. Rev.125, 397(1962). 188.- [105] ‘Non-Abelian Gauge Fields. Commutation Relations’, Phys. Rev.125, 1043 (1962)..- [106] ‘Exterior Algebra and the Action Principle. I’, Proc. Natl. Acad. Sci., U.S.A.48, 603 (1962)..- [107] ‘Non-Abelian Gauge Fields. Relativistic Invariance’, Phys. Rev.127, 324(1962)..- [108] ‘Gauge Invariance and Mass. II’, Phys. Rev.128, 2425 (1962)..- [109] ‘Quantum Variables and Group Parameters’, IlNuovo Cimento30, 278(1963)..- [111] ‘Commutation Relations and Conservation Laws’, Phys. Rev.130, 406 (1963)..- [112] ‘Energy and Momentum Density in Field Theory’, Phys. Rev.130, 800(1963)..- [114] ‘Quantized Gravitational Field.II’ Phys. Rev.132, 1317(1963)..- [116] ‘Coulomb Green’s Function’, J. Math. Phys.5, 1606 (1964)..- [117] ‘Non-Abelian Vector Gauge Fields and the Electromagnetic Field’, Rev. Mod. Phys.26, 609 (1964)..- [118] ‘Field Theory of Matter’, Phys. Rev.135, B816 (1964)..- [124] ‘Field Theory of Matter. II’, Phys. Rev.136, B1821 (1964)..- [128] ‘Field Theory of Matter.IV’, Phys. Rev.140, B158 (1965)..- [132] ‘Relativistic Quantum Field Theory’, Nobel Lecture, in Nobel Lectures — Physics, 1963–1970, Elsevier, Amsterdam, 1972..- [135] ‘Particles and Sources’, Phys. Rev.152, 1219 (1966)..- [137] ‘Chiral Dynamics’, Phys. Letters24B, 473 (1967)..- [139] ‘Partial Symmetry’, Phys. Rev. Letters18, 923 (1967)..- [144] ‘Gauge Fields, Sources and Electromagnetic Masses’, Phys. Rev.165, 1714 (1968); Phys. Rev.167, 1546 (1968)..- [147] ‘Sources and Magnetic Charge’, Phys. Rev.173, 1536 (1968)..- [150] ‘A Magnetic Model of Matter’, Science, 165, 757(1969)..- [151] ‘Theory of Sources’, Contemporary Physics (Trieste Symposium 1968), IAEA Vienna, 1969, Vol. II, p. 59..- [155] ‘How Massive is the W Particle?’, Phys. Rev.D7, 908 (1973)..- [156] ‘Classical Radiation of Accelerated Electrons. II. A Quantum Viewpoint’, Phys. Rev.D7, 1696 (1973)..- [157] ‘How to Avoid ?Y=1Neutral Currents’, Phys. Rev.D8, 960 (1973)..- [160] ‘A Report on Quantum Electrodynamics’, in The Physicist’s Conception of Nature, edited by J. Mehra, Reidel, Dordrecht, 1973, p. 413..- [164] ‘Photon Propagation Function: Spectral Analysis of Its Asymptotic Form’, Proc. Natl. Acad. Sci., U.S.A.71, 3024 (1974)..- [167] ‘Source Theory Viewpoints in Deep Inelastic Scattering’, Proc. Natl. Acad. Sci., U.S.A.72, 1 (1975)..- [172] ‘Magnetic Charge and the Charge Quantization Condition’, Phys. Rev.D12, 3105 (1975)..- [174] ‘Casimir Effect in Source Theory’, Lett. Math. Phys.1, 43 (1975)..- [178] ‘Deep Inelastic Scattering of Leptons’, Proc. Natl. Acad. Sci., U.S.A.73, 3351 (1976)..
£42.74
Springer Theory of Resonances: Principles and Applications
Table of ContentsMathematical and Quantum-Mechanical Background.- General Concepts of the Theory of Resonance States and Processes.- Theory of Resonance States Based on the Hilbert-Schmidt Expansion.- Projection Methods.- Theory of Resonance States and Processes Based on Analytical Continuation in the Coupling Constant.- S-matrix Parametrization of Scattering Data. Extraction of Resonance Parameters from Experimental Data.- Resonances in Atomic Physics.- Conclusion, Open Problems.
£85.49
Springer Solving Frontier Problems of Physics: The Decomposition Method
Book SynopsisThe Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations. Trade Review`I recommend Adomian's new book to all researchers in the area of mathematical modeling and solving complex dynamical systems.' Foundations of Physics, 1994 Table of ContentsPreface. Foreword. 1. On Modelling Physical Phenomena. 2. The Decomposition Method for Ordinary Differential Equations. 3. The Decomposition Method in Several Dimensions. 4. Double Decomposition. 5. Modified Decomposition. 6. Applications of Modified Decomposition. 7. Decomposition Solutions for Neumann Boundary Conditions. 8. Integral Boundary Conditions. 9. Boundary Conditions at Infinity. 10. Integral Equations. 11. Nonlinear Oscillations in Physical Systems. 12. Solution of the Duffing Equation. 13. Boundary-Value Problems with Closed Irregular Contours or Surfaces. 14. Applications in Physics. Appendix I: Padé and Shanks Transform. Appendix II: On Staggered Summation of Double Decomposition Series. Appendix III: Cauchy Products of Infinite Series. Index.
£85.49
Springer Fundamental Problems in Quantum Physics
Book SynopsisFor many physicists quantum theory contains strong conceptual difficulties, while for others the apparent conclusions about the reality of our physical world and the ways in which we discover that reality remain philosophically unacceptable. This book focuses on recent theoretical and experimental developments in the foundations of quantum physics, including topics such as the puzzles and paradoxes which appear when general relativity and quantum mechanics are combined; the emergence of classical properties from quantum mechanics; stochastic electrodynamics; EPR experiments and Bell's Theorem; the consistent histories approach and the problem of datum uniqueness in quantum mechanics; non-local measurements and teleportation of quantum states; quantum non-demolition measurements in optics and matter wave properties observed by neutron, electron and atomic interferometry. Audience: This volume is intended for graduate students of physics and those interested in the foundations of quantum theory.Table of Contents1. The subject of our discussions; E. Santos. 2. Measurement of the Schrödinger wave of a single particle; Y. Aharonov, L. Vaidman. 3. The emergence of classical properties from quantum mechanics: New problems from old; L.E. Ballentine. 4. Deformations of space-time symmetries and fundamental scales; A. Ballesteros, et al. 5. Aspects of quantum reality; S. Bergia. 6. Kochen-Specker diagram of the Peres--Mermin example; A. Cabello. 7. Zeropoint waves and quantum particles; A.M. Cetto, L. de la Peña. 8. Results of atom interferometry experiments with potassium; J.F. Clauser. 9. On the uncertainty relations; J.R. Croca. 10. Continuously diagonalized density operator of open systems; L. Diósi. 11. The hazy spacetime of the Károlyházy model of quantum mechanics; A. Frenkel. 12. Can the experiments based on parametric-down conversion disprove Einstein locality? A. Garuccio. 13. Quantum-mechanical histories and the uncertainty principle; J.J. Halliwell. 14. Experiments with coherent electron wave packets; F. Hasselbach. 15. The ontological interpretation of quantum field theory applied in a cosmological context; B.J. Hiley, A.H. Aziz Muft. 16. State vector reduction via spacetime imprecision; F. Károlyházy. 17. Analyses of classical and thermodynamic limits of quantum mechanics and quantum measurements on the basis of nonstandard analysis; T. Kobayashi. 18. A realistic interpretation of lattice gauge theories; M. Lorente. 19. Is there abridge connecting stochastic and quantum electrodynamics? T.W. Marshall. 20. Action-angle variables inherent in quantum dynamics; J. Martínez-Linares. 21. A philosopher struggles to understand quantum theory: Particle creations and wavepacket reduction; N. Maxwell. 22. Consistent histories and the interpretation of quantum mechanics; R. Omnès. 23. Is quantum mechanics a limit cycle theory? L. de la Peña, A.M. Cetto. 24. Realization and characterization of quantum nondemolition measurements in optics; J.Ph. Poizat, et al. 25. Fuzzy sets and infinite-valued Łukasiewicz logic in foundations of quantum mechanics; J. Pykacz. 26. A model of topological quantization of the electromagnetic field; A.F. Rañada. 27. Postselection and squeezing in neutron interferometry and EPR-experiments; H. Rauch. 28. Macroscopic decoherence and classical stochastic gravity; J.L. Sanchez-Gomez. 29. Dynamics and measurement of the absolute phase in macroscopic quantum systems; F. Sols, R.A. Hegstrom. 30. Realistic quantum theory and relativity; E.J. Squires. 31. On the empirical law of epistemology: Physics as an artifact of mathematics; N.A. Tambakis. 32. Search of a first principle for quantum physics; A.C. de la Torre. 33. Decoherence in an isolated macroscopic quantum system: A parameter-free model involving gravity; J. Unturbe. 34. Nonlocal measurements and teleportation of quantum states; L. Vaidman. 35. Quantum noise in optical photon detectors; A. Vidiella-Barranco, E. Santos.
£123.49
Springer General Relativity and Matter: A Spinor Field Theory from Fermis to Light-Years
Book SynopsisThere exist essentially two levels of investigation in theoretical physics. One is primarily descriptive, concentrating as it does on useful phenomenological approaches toward the most economical classifications of large classes of experimental data on particular phenomena. The other, whose thrust is explanatory, has as its aim the formulation of those underlying hypotheses and their mathematical representations that are capable of furnishing, via deductive analysis, predictions - constituting the particulars of universals (the asserted laws)- about the phenomena under consideration. The two principal disciplines of contemporary theoretical physics - quantum theory and the theory of relativity - fall basically into these respective categories. General Relativity and Matter represents a bold attempt by its author to formulate, in as transparent and complete a way as possible, a fundamental theory of matter rooted in the theory of relativity - where the latter is viewed as providing an explanatory level of understanding for probing the fundamental nature ofmatter indomainsranging all the way fromfermis and lessto light years and more. We hasten to add that this assertion is not meant to imply that the author pretends with his theory to encompass all ofphysics or even a tiny part of the complete objective understanding of our accessible universe. But he does adopt the philosophy that underlying all natural phenomena there is a common conceptualbasis,and then proceeds to investigate how far such a unified viewcan take us at its present stage of development.Trade Review`...to read it should be a rewarding experience for anyone who is concerned with understanding the most fundamental features of the physicist's world view. ...well written and contains some very useful material on both the conceptual and technical aspects of relativity.' Foundations of Physics, 15 (1985) Table of ContentsA.- 1 / Concepts.- B : Mathematical Preliminaries.- 2 / Vector-Tensor Analysis in Relativity Theory.- 3 / Spinor-Quaternion Analysis in Relativity Theory.- C: The Field Equations.- 4 / The Matter Field Equations.- 5 / The Electromagnetic Field Equations.- 6 / The Gravitational Field Equations and Unification with Inertia and Electromagnetism.- 7 / Astrophysics and Cosmology.- Selections from the Author’s Bibliography.
£123.49
Fingerprint! Publishing The Principia
Book SynopsisA groundbreaking work in the field of physics and mathematics. In this monumental work, Newton formulated the laws of motion and universal gravitation, laying the foundation for classical mechanics and revolutionizing our understanding of the physical world. The Principia remains one of the most significant scientific books ever written, influencing generations of scientists, and shaping the course of modern physics and mathematics. The Groundbreaking Work of Sir Isaac Newton Mathematical proofs and equations. Comprehensive coverage of planetary motion. Helps in understanding the principles of motion. Logical and rigorous approach to scientific inquiry. Studied and revered as a seminal work in the field of science.
£13.49
Springer Particles and Fundamental Interactions: An Introduction to Particle Physics
Book SynopsisThe book provides theoretical and phenomenological insights on the structure of matter, presenting concepts and features of elementary particle physics and fundamental aspects of nuclear physics. Starting with the basics (nomenclature, classification, acceleration techniques, detection of elementary particles), the properties of fundamental interactions (electromagnetic, weak and strong) are introduced with a mathematical formalism suited to undergraduate students. Some experimental results (the discovery of neutral currents and of the W± and Z0 bosons; the quark structure observed using deep inelastic scattering experiments) show the necessity of an evolution of the formalism. This motivates a more detailed description of the weak and strong interactions, of the Standard Model of the microcosm with its experimental tests, and of the Higgs mechanism. The open problems in the Standard Model of the microcosm and macrocosm are presented at the end of the book. Table of ContentsPreface.- 1. Historical Notes and Fundamental Concepts.- 2. Particle Interactions with Matter and Detectors.- 3. Particle Accelerators and Particle Detection.- 4. The Paradigm of Interactions: the Electromagnetic Case.- 5. First Discussion of the Other Fundamental Interactions.- 6 Invariance and Conservation Principles.- 7. Hadron Interactions at Low Energies and the Static Quark Model.- 8. Weak Interactions and Neutrinos.- 9. Discoveries in Electron-Positron Collisions.- 10. High Energy Interactions at the Dynamic Quark Model.- 11. The Standard Model of the Microcosm.- 12. CP-Violation and Particle Oscillations.- 13. Microcosm and Macrocosm.- 14. Fundamental aspects of Nucleon Interactions.- Appendix 1. Periodic Table.- Appendix 2. The natural units in subnuclear physics.- Appendix 3. Basic concepts of relativity and classical EM.- Appendix 4. Dirac’s equation and formalism.- Appendix 5. Physical and astrophysical constants.- References.- Index.
£56.99
Springer Flux-Corrected Transport: Principles, Algorithms, and Applications
Book SynopsisAddressing students and researchers as well as Computational Fluid Dynamics practitioners, this book is the most comprehensive review of high-resolution schemes based on the principle of Flux-Corrected Transport (FCT). The foreword by J.P. Boris and historical note by D.L. Book describe the development of the classical FCT methodology for convection-dominated transport problems, while the design philosophy behind modern FCT schemes is explained by S.T. Zalesak. The subsequent chapters present various improvements and generalizations proposed over the past three decades. In this new edition, recent results are integrated into existing chapters in order to describe significant advances since the publication of the first edition. Also, 3 new chapters were added in order to cover the following topics: algebraic flux correction for finite elements, iterative and linearized FCT schemes, TVD-like flux limiters, acceleration of explicit and implicit solvers, mesh adaptation, failsafe limiting for systems of conservation laws, flux-corrected interpolation (remapping), positivity preservation in RANS turbulence models, and the use of FCT as an implicit subgrid scale model for large eddy simulations.Table of ContentsThe conception, gestation, birth and infancy of FCT.- The design of flux-corrected transport (FCT) algorithms for structured grids.- On monotonically integrated large eddy simulation of tubulent flows based on FCT algorithms.- Large scale urban simulations with FCT.- 30 years of FCT.- Algebraic flux corretion I.- Algebraic flux correction II.- Algebraic flux correction III.- Algebraic flux correction IV.- An evaluation of the FCT method for high-speed flows.- Flux-corrected and optimization-based remap.
£42.74
Springer Automatic trend estimation
Book SynopsisOur book introduces a method to evaluate the accuracy of trend estimation algorithms under conditions similar to those encountered in real time series processing. This method is based on Monte Carlo experiments with artificial time series numerically generated by an original algorithm. The second part of the book contains several automatic algorithms for trend estimation and time series partitioning. The source codes of the computer programs implementing these original automatic algorithms are given in the appendix and will be freely available on the web. The book contains clear statement of the conditions and the approximations under which the algorithms work, as well as the proper interpretation of their results. We illustrate the functioning of the analyzed algorithms by processing time series from astrophysics, finance, biophysics, and paleoclimatology. The numerical experiment method extensively used in our book is already in common use in computational and statistical physics.Table of ContentsDiscrete stochastic processes and time series.- Trend definition.- Finite AR(1) stochastic process.- Monte Carlo experiments. - Monte Carlo statistical ensembles.- Numerical generation of trends.- Numerical generation of noisy time series.- Statistical hypothesis testing.- Testing the i.i.d. property.- Polynomial fitting.- Linear regression.- Polynomial fitting.- Polynomial fitting of artificial time series.- An astrophysical example.- Noise smoothing.- Moving average.- Repeated moving average (RMA).- Smoothing of artificial time series.- A financial example.- Automatic estimation of monotonic trends.- Average conditional displacement (ACD) algorithm.- Artificial time series with monotonic trends.- Automatic ACD algorithm.- Evaluation of the ACD algorithm.- A paleoclimatological example.- Statistical significance of the ACD trend.- Time series partitioning.- Partitioning of trends into monotonic segments.- Partitioning of noisy signals into monotonic segments.- Partitioning of a real time series.- Estimation of the ratio between the trend and noise.- Automatic estimation of arbitrary trends.- Automatic RMA (AutRMA).- Monotonic segments of the AutRMA trend.- Partitioning of a financial time series.
£37.99
Springer Noncommutative Geometry and Particle Physics
Book SynopsisThis book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.Table of ContentsPreface.- Introduction.- Part 1. Noncommutative geometric spaces.- Finite noncommutative spaces.- Finite real noncommutative spaces.- Noncommutative Riemannian spin manifolds.- The local index formula in noncommutative geometry.- Part 2. Noncommutative geometry and gauge theories.- Gauge theories from noncommutative manifolds.- Spectral invariants.- Almost-commutative manifolds and gauge theories.- The noncommutative geometry of electrodynamics.- The noncommutative geometry of Yang-Mills fields.- The noncommutative geometry of the Standard Model.- Phenomenology of the noncommutative Standard Model.- Bibliography.
£49.99
Atlantis Press (Zeger Karssen) Lectures on the Mathematics of Quantum Mechanics
Book SynopsisThe first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.Trade Review“QM has also been the source of many interesting mathematical problems and developments to which only very few books devote careful attention and discussion. One of the praiseworthy merits of Dell'Antonio's book is to present a comprehensive and updates account of such important mathematical results. … For these reasons the book qualifies as a must for the education of mathematical physics graduate students and clearly provides very useful information also for theoretical physicists as well for mathematicians.” (Franco Strocchi, zbMATH 1357.81001, 2017)“This is a huge book on the mathematical foundations of quantum theory, including both non-relativistic quantum mechanics (QM) and quantum field theories (QFT). … the specialized reader will find in the book a very nice reference for checking concepts and ways of proceedings in these domains. It is a remarkable book.” (Décio Krause, Mathematical Reviews, May, 2016)Table of ContentsElements of the history of Quantum Mechanics I.- Elements of the history of Quantum Mechanics II.- Axioms, states, observables, measurement, difficulties.- Entanglement, decoherence, Bell’s inequalities, alternative theories.- Automorphisms; Quantum dynamics; Theorems of Wigner, Kadison, Segal; Continuity andgenerators.- Operators on Hilbert spaces I; Basic elements.- Quadratic forms.- Properties of free motion, Anholonomy,Geometric phase.- Elements of C ∗-algebras, GNS representation,automorphisms and dynamical systems.- Derivations and generators. K.M.S. condition. Elements of modular structure. Standard form.- Semigroups and dissipations. Markov approximation.- Quantum dynamical semigroups I.- Positivity preserving contraction semigroups on C ∗-algebras.- Conditional expectations.- Complete Dissipations.- Weyl system, Weyl algebra, lifting symplectic maps.- Magnetic Weyl algebra.- A Theorem of Segal.- Representations of Bargmann, Segal, Fock.- Second quantization.- Other quantizations (deformation, geometric).
£89.99
Atlantis Press (Zeger Karssen) Lyapunov Exponents of Linear Cocycles:
Book SynopsisThe aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for quantities related to the iterates of the base and fiber dynamics associated with the linear cocycle. We establish such estimates for various models of random and quasi-periodic cocycles. Our method has its origins in a paper of M. Goldstein and W. Schlag. Our present work expands upon their approach in both depth and breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach.Trade Review“The effort of the authors to make this text self-contained and to make the exposition very clear and delightful was successful, making this monograph an excellent contribution for both graduate student and anyone interested in the continuity of Lyapunov Exponents.” (Paulo Varandas, Mathematical Reviews, June, 2018)Table of ContentsIntroduction.- Estimates on Grassmann Manifolds.- Abstract Continuity of Lyapunov Exponents.- The Oseledets Filtration and Decomposition.- Large Deviations for Random Cocycles.- Large Deviations for Quasi-Periodic Cocycles.- Further Related Problems.
£63.90
Atlantis Press (Zeger Karssen) Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model
Book SynopsisMean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.Table of Contents
£67.45
World Scientific Publishing Co Pte Ltd Mathematical Methods For Physicists
Book SynopsisThe book covers different aspects of mathematical methods for Physics. It is designed for graduate courses but a part of it can also be used by undergraduate students. The leitmotiv of the book is the search for a common mathematical framework for a wide class of apparently disparate physical phenomena. An important role, within this respect, is provided by a nonconventional formulation of special functions and polynomials. The proposed methods simplify the understanding of the relevant technicalities and yield a unifying view to their applications in Physics as well as other branches of science.The chapters are not organized through the mathematical study of specific problems in Physics, rather they are suggested by the formalism itself. For example, it is shown how the matrix formalism is useful to treat ray Optics, atomic systems evolution, QED, QCD and Feynman diagrams. The methods presented here are simple but rigorous. They allow a fairly substantive tool of analysis for a variety of topics and are useful for beginners as well as the more experienced researchers.
£52.25
World Scientific Publishing Co Pte Ltd Mathematical Methods Of Theoretical Physics
Book Synopsis'This book could serve either as a good reference to remind students about what they have seen in their completed courses or as a starting point to show what needs more investigation. Svozil (Vienna Univ. of Technology) offers a very thorough text that leaves no mathematical area out, but it is best described as giving a synopsis of each application and how it relates to other areas … The text is organized well and provides a good reference list. Summing Up: Recommended. Upper-division undergraduates and graduate students.'CHOICEThis book contains very explicit proofs and demonstrations through examples for a comprehensive introduction to the mathematical methods of theoretical physics. It also combines and unifies many expositions of this subject, suitable for readers with interest in experimental and applied physics.
£66.50
World Scientific Publishing Co Pte Ltd Infinite Dimensional And Finite Dimensional
Book SynopsisThis volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
£85.50
World Scientific Publishing Co Pte Ltd Mathematical Feynman Path Integrals And Their
Book SynopsisFeynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics.This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added.This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists.Table of ContentsIntroduction; A Unified View of Infinite Dimensional Integration; Infinite Dimensional Oscillatory Integrals; Feynman Path Integrals and the Schroedinger Equation; The Stationary Phase Method and the Semiclassical Limit of Quantum Mechanics; Beyond Schroedinger Equation. Further Applications of Feynman Integration; Approaches to Feynman Path Integration; Appendix;
£76.00
World Scientific Publishing Co Pte Ltd Algebraic Structures In Integrability: Foreword
Book SynopsisRelationships of the theory of integrable systems with various branches of mathematics are extremely deep and diverse. On the other hand, the most fundamental exactly integrable systems often have applications in theoretical physics. Therefore, many mathematicians and physicists are interested in integrable models.The book is intelligible to graduate and PhD students and can serve as an introduction to separate sections of the theory of classical integrable systems for scientists with algebraic inclinations. For the young, the book can serve as a starting point in the study of various aspects of integrability, while professional algebraists will be able to use some examples of algebraic structures, which appear in the theory of integrable systems, for wide-ranging generalizations.The statements are formulated in the simplest possible form. However, some ways of generalization are indicated. In the proofs, only essential points are mentioned, while for technical details, references are provided. The focus is on carefully selected examples. In addition, the book proposes many unsolved problems of various levels of complexity. A deeper understanding of every chapter of the book may require the study of more rigorous and specialized literature.
£112.50
World Scientific Publishing Co Pte Ltd Lectures On The Non-equilibrium Theory Of
Book SynopsisThis book discusses in depth many of the key problems in non-equilibrium physics. Besides the standard subjects (Boltzmann and Master equations, linear response) it includes several new important subjects as well. The origin of macroscopic irreversible (dissipative) behavior receives an extended attention and is illustrated in the framework of solvable classical models of open systems (Chapter 3). The scaling relationship between the kinetic and hydrodynamical levels is described in Chapter 9. The QED of charged non-relativistic particles and its restriction to the states without photons to order 1/c² leading to the current-current magnetic interaction is discussed in some depth in Chapters 14 and 15. Bose-Einstein condensation in real time within the frame of rate equations, as well as soliton-like solutions of the non-linear Gross-Pitaevskii equation are discussed in Chapter 22. The presentation also includes the latest developments — quantum kinetics — related to modern ultrafast spectroscopy (Chapters 23-30).This second edition was improved, restructured, and enriched with new results from the recent papers of the author. Chapter 3 was largely extended and Chapters 14 and 15 are completely new. Chapter 22 has a new Section. Several new useful figures were added throughout the book as well.
£85.50
World Scientific Publishing Co Pte Ltd Mathematical Journey Through Differential
Book SynopsisMathematics is the language of physics, and over time physicists have developed their own dialect. The main purpose of this book is to bridge this language barrier, and introduce the readers to the beauty of mathematical physics. It shows how to combine the strengths of both approaches: physicists often arrive at interesting conjectures based on good intuition, which can serve as the starting point of interesting mathematics. Conversely, mathematicians can more easily see commonalities between very different fields (such as quantum mechanics and electromagnetism), and employ more advanced tools.Rather than focusing on a particular topic, the book showcases conceptual and mathematical commonalities across different physical theories. It translates physical problems to concrete mathematical questions, shows how to answer them and explains how to interpret the answers physically. For example, if two Hamiltonians are close, why are their dynamics similar?The book alternates between mathematics- and physics-centric chapters, and includes plenty of concrete examples from physics as well as 76 exercises with solutions. It exploits that readers from either end are familiar with some of the material already. The mathematics-centric chapters provide the necessary background to make physical concepts mathematically precise and establish basic facts. And each physics-centric chapter introduces physical theories in a way that is more friendly to mathematicians.As the book progresses, advanced material is sprinkled in to showcase how mathematics and physics augment one another. Some of these examples are based on recent publications and include material which has not been covered in other textbooks. This is to keep it interesting for the readers.
£112.50
World Scientific Publishing Co Pte Ltd Mathematical Journey Through Differential
Book SynopsisMathematics is the language of physics, and over time physicists have developed their own dialect. The main purpose of this book is to bridge this language barrier, and introduce the readers to the beauty of mathematical physics. It shows how to combine the strengths of both approaches: physicists often arrive at interesting conjectures based on good intuition, which can serve as the starting point of interesting mathematics. Conversely, mathematicians can more easily see commonalities between very different fields (such as quantum mechanics and electromagnetism), and employ more advanced tools.Rather than focusing on a particular topic, the book showcases conceptual and mathematical commonalities across different physical theories. It translates physical problems to concrete mathematical questions, shows how to answer them and explains how to interpret the answers physically. For example, if two Hamiltonians are close, why are their dynamics similar?The book alternates between mathematics- and physics-centric chapters, and includes plenty of concrete examples from physics as well as 76 exercises with solutions. It exploits that readers from either end are familiar with some of the material already. The mathematics-centric chapters provide the necessary background to make physical concepts mathematically precise and establish basic facts. And each physics-centric chapter introduces physical theories in a way that is more friendly to mathematicians.As the book progresses, advanced material is sprinkled in to showcase how mathematics and physics augment one another. Some of these examples are based on recent publications and include material which has not been covered in other textbooks. This is to keep it interesting for the readers.
£66.50
World Scientific Publishing Co Pte Ltd Scale Transitions As Foundations Of Physics
Book SynopsisThe scale transitions are essential to physical knowledge. The book describes the history of essential moments of physics, viewed as necessary consequences of the unavoidable process of scale transition, and provides the mathematical techniques for the construction of a theoretical physics founded on scale transition. The indispensable mathematical technique is analyticity, helping in the construction of space coordinate systems. The indispensable theoretical technique from physical point of view is the affine theory of surfaces. The connection between the two techniques is provided by a duality in defining the physical properties.
£112.50
World Scientific Publishing Co Pte Ltd Spiritual Insights From The New Science: Complex
Book SynopsisSpiritual Insights from the New Science is a guide to the deep spiritual wisdom drawn from one of the newest areas of science — the study of complex systems. The author, a former research scientist with over three decades of experience in the field of complexity science, tells her story of being attracted, as a young student, to the study of self-organizing systems where she encountered the strange and beautiful topics of chaos, fractals and other concepts that comprise complexity science. Using the events of her life, she describes lessons drawn from this science that provide insights into not only her own life, but all our lives. These insights show us how to weather the often disruptive events we all experience when growing and changing.The book goes on to explore, through the unfolding story of the author's life as a practicing scientist, other key concepts from the science of complex systems: cycles and rhythms, attractors and bifurcations, chaos, fractals, self-organization, and emergence. Examples drawn from religious rituals, dance, philosophical teachings, mysticism, native American spirituality, and other sources are used to illustrate how these scientific insights apply to all aspects of life, especially the spiritual. Spiritual Insights from the New Science shows the links between this new science and our human spirituality and presents, in engaging, accessible language, the argument that the study of nature can lead to a better understanding of the deepest meaning of our lives.
£61.75
World Scientific Publishing Co Pte Ltd Spiritual Insights From The New Science: Complex
Book SynopsisSpiritual Insights from the New Science is a guide to the deep spiritual wisdom drawn from one of the newest areas of science — the study of complex systems. The author, a former research scientist with over three decades of experience in the field of complexity science, tells her story of being attracted, as a young student, to the study of self-organizing systems where she encountered the strange and beautiful topics of chaos, fractals and other concepts that comprise complexity science. Using the events of her life, she describes lessons drawn from this science that provide insights into not only her own life, but all our lives. These insights show us how to weather the often disruptive events we all experience when growing and changing.The book goes on to explore, through the unfolding story of the author's life as a practicing scientist, other key concepts from the science of complex systems: cycles and rhythms, attractors and bifurcations, chaos, fractals, self-organization, and emergence. Examples drawn from religious rituals, dance, philosophical teachings, mysticism, native American spirituality, and other sources are used to illustrate how these scientific insights apply to all aspects of life, especially the spiritual. Spiritual Insights from the New Science shows the links between this new science and our human spirituality and presents, in engaging, accessible language, the argument that the study of nature can lead to a better understanding of the deepest meaning of our lives.
£23.75
World Scientific Publishing Co Pte Ltd Analytic Hyperbolic Geometry And Albert
Book SynopsisThis book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. The premise of analogy as a study strategy is to make the unfamiliar familiar. Accordingly, this book introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors. Gyrovectors turn out to be equivalence classes that add according to the gyroparallelogram law just as vectors are equivalence classes that add according to the parallelogram law. In the gyrolanguage of this book, accordingly, one prefixes a gyro to a classical term to mean the analogous term in hyperbolic geometry. As an example, the relativistic gyrotrigonometry of Einstein's special relativity is developed and employed to the study of the stellar aberration phenomenon in astronomy.Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. It turns out that the invariant mass of the relativistic center of mass of an expanding system (like galaxies) exceeds the sum of the masses of its constituent particles. This excess of mass suggests a viable mechanism for the formation of dark matter in the universe, which has not been detected but is needed to gravitationally 'glue' each galaxy in the universe. The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying hyperbolic geometry.
£162.00
World Scientific Publishing Co Pte Ltd Gentle Introduction To Knots, Links And Braids, A
Book SynopsisThe interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.
£85.50
World Scientific Publishing Co Pte Ltd Lectures On Quantum Mechanics And Attractors
Book SynopsisThis book gives a concise introduction to Quantum Mechanics with a systematic, coherent, and in-depth explanation of related mathematical methods from the scattering theory and the theory of Partial Differential Equations.The book is aimed at graduate and advanced undergraduate students in mathematics, physics, and chemistry, as well as at the readers specializing in quantum mechanics, theoretical physics and quantum chemistry, and applications to solid state physics, optics, superconductivity, and quantum and high-frequency electronic devices.The book utilizes elementary mathematical derivations. The presentation assumes only basic knowledge of the origin of Hamiltonian mechanics, Maxwell equations, calculus, Ordinary Differential Equations and basic PDEs. Key topics include the Schrödinger, Pauli, and Dirac equations, the corresponding conservation laws, spin, the hydrogen spectrum, and the Zeeman effect, scattering of light and particles, photoelectric effect, electron diffraction, and relations of quantum postulates with attractors of nonlinear Hamiltonian PDEs. Featuring problem sets and accompanied by extensive contemporary and historical references, this book could be used for the course on Quantum Mechanics and is also suitable for individual study.
£72.00
World Scientific Publishing Co Pte Ltd Gentle Introduction To Knots, Links And Braids, A
Book SynopsisThe interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.
£52.25
World Scientific Publishing Co Pte Ltd Special Functions Of Fractional Calculus:
Book SynopsisThis book aims to provide an overview of the special functions of fractional calculus and their applications in diffusion and random search processes. The book contains detailed calculations for various examples of anomalous diffusion, random search and stochastic resetting processes, which can be easily followed by the reader, who will be able to reproduce the obtained results. The book will be intended for advanced undergraduate and graduate students and researchers in physics, mathematics and other natural sciences due to the various examples which will be provided in the book.
£85.50
World Scientific Publishing Co Pte Ltd Algebraic Bethe Ansatz And Correlation Functions:
Book SynopsisIt is unlikely that today there is a specialist in theoretical physics who has not heard anything about the algebraic Bethe ansatz. Over the past few years, this method has been actively used in quantum statistical physics models, condensed matter physics, gauge field theories, and string theory.This book presents the state-of-the-art research in the field of algebraic Bethe ansatz. Along with the results that have already become classic, the book also contains the results obtained in recent years. The reader will get acquainted with the solution of the spectral problem and more complex problems that are solved using this method. Various methods for calculating scalar products and form factors are described in detail. Special attention is paid to applying the algebraic Bethe ansatz to the calculation of the correlation functions of quantum integrable models. The book also elaborates on multiple integral representations for correlation functions and examples of calculating the long-distance asymptotics of correlations.This text is intended for advanced undergraduate and postgraduate students, and specialists interested in the mathematical methods of studying physical systems that allow them to obtain exact results.
£121.50
World Scientific Publishing Co Pte Ltd Guide To The Umbral Calculus, A Different
Book SynopsisThis book covers different aspects of umbral calculus and of its more recent developments. It discusses the technical details in depth, including its relevant applications. The book has therefore manyfold scopes to introduce a mathematical tool, not widespread known as it should be; to present a complete account of the relevant capabilities through the use of different examples of applications; to provide a formal bridge between different fields of research in pure and applied.
£90.00
World Scientific Publishing Co Pte Ltd Renormalized Perturbation Theory And Its
Book SynopsisThe results of renormalized perturbation theory, in QCD and other quantum field theories, are ambiguous at any finite order, due to renormalization-scheme dependence. The perturbative results depend upon extraneous scheme variables, including the renormalization scale, that the exact result cannot depend on. Such 'non-invariant approximations' occur in many other areas of physics, too. The sensible strategy is to find where the approximant is stationary under small variations of the extraneous variables. This general principle is explained and illustrated with various examples. Also dimensional transmutation, RG equations, the essence of renormalization and the origin of its ambiguities are explained in simple terms, assuming little or no background in quantum field theory. The minimal-sensitivity approach leads to 'optimized perturbation theory,' which is developed in detail. Applications to Re⁺e⁻, the infrared limit, and to the optimization of factorized quantities, are also discussed thoroughly.
£85.50
World Scientific Publishing Co Pte Ltd Set Theory And Its Applications In Physics And
Book SynopsisWhy learn set theory? This book provides the answer — it is interesting, and also useful! Taking a new approach and looking from a fresh perspective, the discussion flows in a friendly and transparent way, supplemented with a lot of examples and figures. This makes the theory easily comprehensible: the proofs get vivid and visual, enveloped with interesting applications for students in (applied) math, physics, and engineering. Given the theory and the applications, the book could serve as a textbook in four (undergraduate) math courses: Introduction to set theory and its application; Chaos theory and stability — a geometrical point of view; Functional analysis — Han-Banach theory; and Cryptography with quantum computing. It teaches set theory from the basics, including the axiom of choice, the well ordering theorem, and Zorn's lemma. Furthermore, it uses Cantor's set to introduce chaos theory from a geometrical point of view. Moreover, it introduces the binomial formula (and other related formulas), and uses them in quantum statistical mechanics. And finally, it uses Zorn's lemma in functional analysis, general relativity, and quantum mechanics. There are also practical applications in cryptography, error correction, quantum computing and programming.
£108.00
World Scientific Publishing Co Pte Ltd Nonlinear Field Theories And Unexplained
Book SynopsisThe book is devoted to several topical questions in modern mathematical and theoretical physics, astrophysics, geophysics, and cosmology that remain unsolved within the framework of the standard approaches. To them, one can attribute unexplained properties of the magnetic fields of stars and planets, puzzles of the Earth's atmosphere, the phenomenon of ball lightning, the problem of a qualitative description for nuclear forces and their well-known property of saturation, enigmatic properties of spiral galaxies, the problem of the cosmological singularity, mysteries of the dark matter and dark energy, amongst others. To find theoretical ways for understanding such phenomena, new nonlinear generalizations of the classical field theories and advanced methods to solve nonlinear equations arising in them are studied and presented in this book.
£99.00
World Scientific Publishing Co Pte Ltd State-sum Models Of Piecewise Linear Quantum
Book SynopsisThis book gives a description of state-sum quantum gravity models which are based on triangulations of a smooth spacetime manifold. It contains detailed descriptions of Regge quantum gravity, spin-foam models and spin-cube models. Some other similar models, like the dynamical triangulations models, are only briefly described, since the sum over the spacetime triangulations is outside the scope of this book.The book also contains a detailed description of the approach where the piecewise linear (PL) manifold corresponding to a smooth manifold triangulation is considered as the basic structure of the spacetime. Hence the PL structure is not an auxiliary tool used to define the gravitational path integral for a smooth spacetime, but it is taken as a physical property of the spacetime. Consequently, it is straightforward to construct a finite gravitational path integral. Another consequence is that the problems of determination of the classical limit and how to calculate the quantum corrections can be solved by using the effective action method. The smooth manifold limit problem is then replaced by the problem of a smooth manifold approximation for the effective action, which can be obtained by using the standard quantum field theory with a physical cutoff.Some physical effects of a PL spacetime quantum gravity theory are also described, one of which is that the cosmological constant spectrum contains the observed value.A short exposition of higher gauge theory is also given, which is a promising way to generalize a gauge symmetry by using the concept of a 2-group. A 2-group is a categorical generalization of a group, and by using this approach one can construct the spin-cube models of quantum gravity.
£66.50
World Scientific Publishing Co Pte Ltd Quantum Anharmonic Oscillator
Book SynopsisQuartic anharmonic oscillator with potential V(x)= x² + g²x⁴ was the first non-exactly-solvable problem tackled by the newly-written Schrödinger equation in 1926. Since that time thousands of articles have been published on the subject, mostly about the domain of small g² (weak coupling regime), although physics corresponds to g² ~ 1, and they were mostly about energies.This book is focused on studying eigenfunctions as a primary object for any g². Perturbation theory in g² for the logarithm of the wavefunction is matched to the true semiclassical expansion in powers of ℏ: it leads to locally-highly-accurate, uniform approximation valid for any g²∈[0,∞) for eigenfunctions and even more accurate results for eigenvalues. This method of matching can be easily extended to the general anharmonic oscillator as well as to the radial oscillators. Quartic, sextic and cubic (for radial case) oscillators are considered in detail as well as quartic double-well potential.
£90.00
World Scientific Publishing Co Pte Ltd Density Functionals For Many-particle Systems:
Book SynopsisDensity Functional Theory (DFT) first established it's theoretical footing in the 1960s from the framework of Hohenberg-Kohn theorems. DFT has since seen much development in evaluation techniques as well as application in solving problems in Physics, Mathematics and Chemistry.This review volume, part of the IMS Lecture Notes Series, is a collection of contributions from the September 2019 Workshop on the topic, held in the Institute for Mathematical Sciences, National University of Singapore.With contributions from prominent Mathematicians, Physicists, and Chemists, the volume is a blend of comprehensive review articles on the Mathematical and the Physicochemical aspects of DFT and shorter contributions on particular themes, including numerical implementations.The book will be a useful reference for advanced undergraduate and postgraduate students as well as researchers.
£112.50
World Scientific Publishing Co Pte Ltd Finite Temperature Field Theory
Book SynopsisThis book discusses all three formalisms used in the study of finite temperature field theory, namely the imaginary time formalism, the closed time formalism and thermofield dynamics. In addition, the finite temperature description on an arbitrary path in the complex t-plane is also described in detail. Gauge field theories and symmetry restoration at finite temperature are among the practical examples discussed in depth. The thermal operator representation relating the zero temperature Feynman graphs to the finite temperature ones are also explained in depth. Applications of the formalisms are worked out in detail. The consistent generalization of light-front field theories to finite temperature is systematically explained as well as the phenomenon of Unruh radiation. Cutting (Cutcosky) rules for the imaginary parts of amplitudes at finite temperature are discussed in careful detail and examples are worked out. Spontaneous and dynamical symmetry breaking and possible symmetry restoration at finite temperature are described. The question of gauge dependence of the effective potential as well as physical parameters (like mass) and the Nielsen identities are explained with examples. The methods for calculating effective actions at finite temperature are described with examples. The subtleties which arise at finite temperature are pointed out in detail also with examples. The nonrestoration of some of the symmetries at high temperature (such as supersymmetry) and theories on nonsimply connected space-times are described thoroughly. Examples of nonequilibrium phenomena are discussed with the disoriented chiral condensates as an illustration. Fluctuation-dissipation theorem is explained in detail and is worked out systematically for glassy materials. Several appendices are added at the end of some of the chapters to help the readers appreciate the discussions of the individual chapters.This book is a very useful tool for graduate students, teachers and researchers in theoretical physics.
£121.50
World Scientific Publishing Co Pte Ltd Finite Temperature Field Theory
Book SynopsisThis book discusses all three formalisms used in the study of finite temperature field theory, namely the imaginary time formalism, the closed time formalism and thermofield dynamics. In addition, the finite temperature description on an arbitrary path in the complex t-plane is also described in detail. Gauge field theories and symmetry restoration at finite temperature are among the practical examples discussed in depth. The thermal operator representation relating the zero temperature Feynman graphs to the finite temperature ones are also explained in depth. Applications of the formalisms are worked out in detail. The consistent generalization of light-front field theories to finite temperature is systematically explained as well as the phenomenon of Unruh radiation. Cutting (Cutcosky) rules for the imaginary parts of amplitudes at finite temperature are discussed in careful detail and examples are worked out. Spontaneous and dynamical symmetry breaking and possible symmetry restoration at finite temperature are described. The question of gauge dependence of the effective potential as well as physical parameters (like mass) and the Nielsen identities are explained with examples. The methods for calculating effective actions at finite temperature are described with examples. The subtleties which arise at finite temperature are pointed out in detail also with examples. The nonrestoration of some of the symmetries at high temperature (such as supersymmetry) and theories on nonsimply connected space-times are described thoroughly. Examples of nonequilibrium phenomena are discussed with the disoriented chiral condensates as an illustration. Fluctuation-dissipation theorem is explained in detail and is worked out systematically for glassy materials. Several appendices are added at the end of some of the chapters to help the readers appreciate the discussions of the individual chapters.This book is a very useful tool for graduate students, teachers and researchers in theoretical physics.
£76.00
World Scientific Publishing Co Pte Ltd Generation Of Self-excited, Hidden And
Book SynopsisWhat kind of dynamics is a piecewise linear system able to display? How may they generate heteroclinic chaos? How can the coexistence of attractors be designed and characterized? Is it necessary to have equilibrium points to generate chaotic behavior? Chaos theory and complex systems are interesting and evolving topics whose investigation from a theoretical and practical point of view constantly leads to arising questions. Interesting behaviors can be observed in self-excited attractors, hidden attractors and non-self-excited attractors.This book presents some fundamentals of linear system theory and recent approaches to design the three classes of chaotic attractors in piecewise linear systems. Each chapter presents a brief description and basic concepts to provide an overview of linear systems theory; chaos and multistability in integer linear systems; hidden and non-self-excited attractors; and fractional approaches. They also provide example systems to illustrate the concepts and design methods introduced. Some current topics under investigation are addressed from an integer order perspective to make the connection with the fractional order counterpart.This textbook provides a comprehensive introduction, methodologies, and analysis tools to study chaotic piecewise linear systems and will be suitable for undergraduate or graduate students interested in the field of chaos and complex dynamics.
£66.50
World Scientific Publishing Co Pte Ltd Group Theory: Finite Discrete Groups And
Book SynopsisThis book deals with the role played by symmetry in the understanding of the physical world, beginning with the notion of geometric symmetries of the ancient Greek philosophers and mathematicians. The recognition of the existence of symmetries led to the notion of transformations, which led from one state of the system to another. It was then realized that such transformations, under the operation of multiplication, constitute an interesting set, whose study led to the branch of mathematics known as Group Theory. With the emergence of quantum mechanics, this theory became much more interesting and led to some additional applications. The theory got another boost with the need for of the internal degrees of freedom in describing physical systems. This way the notion of symmetry is no longer purely geometric and evolved into a useful tool in the study of all physical sciences.For practical reasons as well as pedagogical reasons, group theory is usually split into two parts. The first deals with discrete groups, with the group elements being countable, usually finite in number, while the second deals with continuous groups, whose elements depend on continuous parameters. This volumefocuses the discussion on discrete groups. Given that group theory should be presented from a unified perspective, involving not only the mathematical rigor and beauty of symmetries, but also the ability to use it as a tool for applications, either currently popular or expected to become so in the future, this approach will surely be more beneficial to the dedicated reader. It is not intended for those who would like to just look up a formula or use the results of a table, without understanding their derivation.
£99.00
World Scientific Publishing Company Macroscopic Electrodynamics An Introductory
Book Synopsis
£162.00
