Gravity Books
Springer Nature Switzerland AG Relativity: A Journey Through Warped Space and Time
Book SynopsisThis primer brilliantly exposes concepts related to special and general relativity for the absolute beginner. It can be used either as an introduction to the subject at a high school level or as a useful compass for undergraduates who want to move the first steps towards Einstein's theories.The book is enhanced throughout with many useful exercises and beautiful illustrations to aid understanding.The topics covered include: Lorentz transformations, length contraction and time dilation, the twin paradox (and other paradoxes), Minkowski spacetime, the Einstein equivalence principle, curvature of space and spacetime, geodesics, parallel transport, Einstein’s equations of general relativity, black holes, wormholes, cosmology, gravitational waves, time machines, and much more.Table of Contents1 Introduction.- 2 Fundamentals of Math & Classical Mechanics.- 3 Special Relativity.- 4 General Relativity.- A Quick Reference.- B Answer to Select Problems.
£52.24
Springer Nature Switzerland AG Applied General Relativity: Theory and
Book SynopsisIn the late 20th and beginning 21st century high-precision astronomy, positioning and metrology strongly rely on general relativity. Supported by exercises and solutions this book offers graduate students and researchers entering those fields a self-contained and exhaustive but accessible treatment of applied general relativity. The book is written in a homogenous (graduate level textbook) style allowing the reader to understand the arguments step by step. It first introduces the mathematical and theoretical foundations of gravity theory and then concentrates on its general relativistic applications: clock rates, clock sychronization, establishment of time scales, astronomical references frames, relativistic astrometry, celestial mechanics and metrology. The authors present up-to-date relativistic models for applied techniques such as Satellite LASER Ranging (SLR), Lunar LASER Ranging (LLR), Globale Navigation Satellite Systems (GNSS), Very Large Baseline Interferometry (VLBI), radar measurements, gyroscopes and pulsar timing. A list of acronyms helps the reader keep an overview and a mathematical appendix provides required functions and terms.Table of Contents
£67.49
Springer Nature Switzerland AG Special Relativity: An Introduction with 200
Book SynopsisThis textbook develops Special Relativity in a systematic way and offers problems with detailed solutions to empower students to gain a real understanding of this core subject in physics. This new edition has been thoroughly updated and has new sections on relativistic fluids, relativistic kinematics and on four-acceleration. The problems and solution section has been significantly expanded and short history sections have been included throughout the book.The approach is structural in the sense that it develops Special Relativity in Minkowski space following the parallel steps as the development of Newtonian Physics in Euclidian space. A second characteristic of the book is that it discusses the mathematics of the theory independently of the physical principles, so that the reader will appreciate their role in the development of the physical theory.The book is intended to be used both as a textbook for an advanced undergraduate teaching course in Special Relativity but also as a reference book for the future. Table of ContentsMathematical Part.- The Structure of the Theories of Physics.- Newtonian Physics.- The Foundation of Special Relativity.- The Physics of the Position Four-Vector.- Relativistic Kinematics.- Four-Acceleration.- Paradoxes.- Mass – Four-Momentum.- Relativistic Reactions.- Four-Force.- Irreducible Decompositions.- The Electromagnetic Field.- Relativistic Angular Momentum.- The Covariant Lorentz Transformation.- Geometric Description of Relativistic Interactions.
£72.56
Springer Nature Switzerland AG Applied Holography: A Practical Mini-Course
Book SynopsisThis primer is a collection of notes based on lectures that were originally given at IIT Madras (India) and at IFT Madrid (Spain). It is a concise and pragmatic course on applied holography focusing on the basic analytic and numerical techniques involved. The presented lectures are not intended to provide all the fundamental theoretical background, which can be found in the available literature, but they concentrate on concrete applications of AdS/CFT to hydrodynamics, quantum chromodynamics and condensed matter. The idea is to accompany the reader step by step through the various benchmark examples with a classmate attitude, providing details for the computations and open-source numerical codes in Mathematica, and sharing simple tricks and warnings collected during the author’s research experience. At the end of this path, the reader will be in possess of all the fundamental skills and tools to learn by him/herself more advanced techniques and to produce independent and novel research in the field.Table of ContentsA Strings-less introduction to AdS-CFT.- A Practical Understanding of the Dictionary.- The first big success: η/s and Hydrodynamics.- Holographic Transport via analytic and numerical techniques.
£52.24
Springer Nature Switzerland AG Introduction to Einstein’s Theory of Relativity:
Book SynopsisThe revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of differential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity. Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations. Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.Table of ContentsNewton’s law of universal gravitation.- The force law of gravitation.- Newton’s law of gravitation in local form.- Tidal forces.- The principle of equivalence.- The general principle of relativity.- The covariance principle.- Mach’s principle.- The special theory of relativity.- Coordinate systems and Minkowski diagrams.- Synchronization of clocks.- The Doppler effect.- Relativistic time-dilation.- The relativity of simultaneity.- The Lorentz contraction.- The Lorentz transformation.- The Lorentz invariant interval.- The twin paradox.- Hyperbolic motion.- Energy and mass.- Relativistic increase of mass.- Tachyons.- Magnetism as a relativistic second order effect.- Vectors, tensors and forms.- Vectors.- Four-vectors.- Tangent vector fields and coordinate vectors.- Coordinate transformations.- Structure coefficients.- Tensors.- Transformation of tensor components.- Transformation of basis 1-forms.- The metric tensor.- Forms.- Rotating and accelerated reference frames.- Rotating reference frames.- The spatial metric tensor.- Angular acceleration of the rotating frame.- Gravitational time dilation.- Path of photons emitted from the axis in a rotating frame.- The Sagnac effect.- Uniformly accelerated reference frames.- Covariant differentiation.- Differentiation of forms.- Exterior differentiation.- Covariant derivative.- The Christoffel symbols.- Geodetic curves.- The covariant Euler-Lagrange equations.- Application of the Lagrange formalism to free particles.- Equation of motion from Lagrange’s equations.- Geodesic worldliness in spacetime.- Gravitational Doppler effect.- The Koszul connection.- Connection coefficients and structure coefficients in a Riemannian (torsion free) space.- Covariant differentiation of vectors, forms and tensors.- Covariant differentiation of a vector field in an arbitrary basis.- Covariant differentiation of forms.- Generalization for tensors of higher rank.- The Cartan connection.- Curvature.- The Riemann curvature tensor.- Differential geometry of surfaces.- Surface curvature using the Cartan formalism.- The Ricci identity.- Bianchi’s 1st identity.- Bianchi’s 2nd identity.- Einstein’s field equations.- Energy-momentum conservation.- Newtonian fluid.- Perfect fluids.- Einstein’s curvature tensor.- Einstein’s field equations.- The 'geodesic postulate' as a consequence of the field equations.- The Schwarschild spacetime.- Schwarzschild’s exterior solution.- Radial free fall in Schwarzschild spacetime.- Light cones in Schwarzschild spacetime.- Analytical extension of the Schwarzschild coordinates.- Embedding of the Schwarzschild metric.- Deceleration of light.- Particle trajectories in Schwarzschild 3-space.- Motion in the equatorial plane.- Classical tests of Einstein’s general theory of relativity.- The Hafele-Keating experiment.- Mercury’s perihelion precession.- Deflection of light.- Black holes.- 'Surface gravity': gravitational acceleration on the horizon of a black hole.- Hawking radiation: radiation from a black hole.- Rotating black holes: The Kerr metric.- Zero-angular-momentum-observers.- Does the Kerr space have a horizon?.- Schwarzschild’s interior solution.- Newtonian incompressible star.- The pressure contribution to the gravitational mass of a static, spherically symmetric system.- The Tolman-Oppenheimer-Volkov equation.- An exact solution for incompressible stars – Schwarzschild’s interior solution.- Cosmology.- Comoving coordinate system.- Curvature isotropy – the Robertson-Walker metric.- Cosmic dynamics.- Hubble’s law.- Cosmological redshift of light.- Cosmic fluids.- Isotropic and homogeneous universe models.- Some cosmological models.- Radiation dominated model.- Dust dominated model.- Transition from radiation to matter dominated universe.- Friegmann-Lemaître model.- Inflationary cosmology.- Problems with the Big Bang models.- Cosmic inflation.
£27.99
Springer Nature Switzerland AG A First Course on Symmetry, Special Relativity and Quantum Mechanics: The Foundations of Physics
Book SynopsisThis book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics.Students are introduced to several topics not typically covered until much later in their education.These include space-time diagrams, the action principle, a proof of Noether's theorem, Lorentz vectors and tensors, symmetry breaking and general relativity. The book also provides extensive descriptions on topics of current general interest such as gravitational waves, cosmology, Bell's theorem, entanglement and quantum computing.Throughout the text, every opportunity is taken to emphasize the intimate connection between physics, symmetry and mathematics.The style remains light despite the rigorous and intensive content. The book is intended as a stand-alone or supplementary physics text for a one or two semester course for students who have completed an introductory calculus course and a first-year physics course that includes Newtonian mechanics and some electrostatics. Basic knowledge of linear algebra is useful but not essential, as all requisite mathematical background is provided either in the body of the text or in the Appendices. Interspersed through the text are well over a hundred worked examples and unsolved exercises for the student.Table of Contents1 Introduction 91.1 The goal of physics . . . . . . . . . . . . . . . . . . . . . . . . 91.2 The connection between physics and mathematics . . . . . . . 101.3 Paradigm shifts . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4 The Correspondence Principle . . . . . . . . . . . . . . . . . . 162 Symmetry and Physics 172.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 172.2 What is Symmetry? . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Role of Symmetry in Physics . . . . . . . . . . . . . . . . . . . 182.3.1 Symmetry as a guiding principle . . . . . . . . . . . . . 182.3.2 Symmetry and Conserved Quantities: Noether's Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.3 Symmetry as a tool for simplifying problems . . . . . . 192.4 Symmetries were made to be broken . . . . . . . . . . . . . . 202.4.1 Spacetime symmetries . . . . . . . . . . . . . . . . . . 202.4.2 Parity violation . . . . . . . . . . . . . . . . . . . . . . 212.4.3 Spontaneously broken symmetries . . . . . . . . . . . . 242.4.4 Variational calculations: Lifeguards and light rays . . . 273 Formal Aspects of Symmetry 303.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Symmetries and Operations . . . . . . . . . . . . . . . . . . . 303.2.1 Denition of a symmetry operation . . . . . . . . . . . 303.2.2 Rules obeyed by symmetry operations . . . . . . . . . 323.2.3 Multiplication tables . . . . . . . . . . . . . . . . . . . 353.2.4 Symmetry and group theory . . . . . . . . . . . . . . . 363.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.1 The identity operation . . . . . . . . . . . . . . . . . . 373.3.2 Permutations of two identical objects . . . . . . . . . . 373.3.3 Permutations of three identical objects . . . . . . . . . 383.3.4 Rotations of regular polygons . . . . . . . . . . . . . . 393.4 Continuous vs discrete symmetries . . . . . . . . . . . . . . . 403.5 Symmetries and Conserved Quantities:Noether's Theorem . . . . . . . . . . . . . . . . . . . . . . . . 413.6 Supplementary: Variational Mechanics and the Proof of Noether'sTheorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.6.1 Variational Mechanics: Principle of Least Action . . . . 423.6.2 Euler-Lagrange Equations . . . . . . . . . . . . . . . . 473.6.3 Proof of Noether's Theorem . . . . . . . . . . . . . . . 484 Symmetries and Linear Transformations 524.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 524.2 Review of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 534.2.1 Coordinate free denitions . . . . . . . . . . . . . . . . 534.2.2 Cartesian Coordinates . . . . . . . . . . . . . . . . . . 584.2.3 Vector operations in component form . . . . . . . . . . 594.2.4 Position vector . . . . . . . . . . . . . . . . . . . . . . 604.2.5 Dierentiation of vectors: velocity and acceleration . . 624.3 Linear Transformations . . . . . . . . . . . . . . . . . . . . . . 634.3.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . 634.3.2 Translations . . . . . . . . . . . . . . . . . . . . . . . . 644.3.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 664.3.4 Reections . . . . . . . . . . . . . . . . . . . . . . . . . 674.4 Linear Transformations and matrices . . . . . . . . . . . . . . 684.4.1 Linear transformations as matrices . . . . . . . . . . . 684.4.2 Identity Transformation and Inverses . . . . . . . . . . 704.4.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 704.4.4 Reections . . . . . . . . . . . . . . . . . . . . . . . . . 724.4.5 Matrix Representation of Permutations of Three Objects 734.5 Pythagoras and Geometry . . . . . . . . . . . . . . . . . . . . 745 Special Relativity I: The Basics 775.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 775.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2.1 Frames5.2.2 Spacetime Diagrams . . . . . . . . . . . . . . . . . . . 785.2.3 Newtonian Relativity and Galilean Transformations . . 835.3 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.3.1 The Fundamental Postulate . . . . . . . . . . . . . . . 855.3.2 The problem with Galilean Relativity . . . . . . . . . . 855.3.3 Michelson-Morley Experiment . . . . . . . . . . . . . . 875.3.4 Maxwell's Equations . . . . . . . . . . . . . . . . . . . 905.4 Summary of Consequences . . . . . . . . . . . . . . . . . . . . 915.5 Relativity of Simultaneity . . . . . . . . . . . . . . . . . . . . 925.6 Time Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.6.1 Derivation: . . . . . . . . . . . . . . . . . . . . . . . . 975.6.2 Proper Time . . . . . . . . . . . . . . . . . . . . . . . . 995.6.3 Experimental Conrmation . . . . . . . . . . . . . . . 1015.6.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 1025.7 Lorentz Contraction . . . . . . . . . . . . . . . . . . . . . . . 1045.7.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . 1045.7.2 Properties: . . . . . . . . . . . . . . . . . . . . . . . . . 1045.7.3 Proper Length and Proper Distance. . . . . . . . . . . 1045.7.4 Examples: . . . . . . . . . . . . . . . . . . . . . . . . . 1056 Special Relativity II: In Depth 1106.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1106.2 Lorentz Transformations . . . . . . . . . . . . . . . . . . . . . 1106.2.1 Derivation of general form . . . . . . . . . . . . . . . . 1106.2.2 Properties of Lorentz Transformations . . . . . . . . . 1136.2.3 Lorentzian Geometry . . . . . . . . . . . . . . . . . . . 1166.3 The Light Cone . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.4 Proper time revisited . . . . . . . . . . . . . . . . . . . . . . . 1206.5 Relativistic Addition of Velocities . . . . . . . . . . . . . . . . 1226.6 Relativistic Doppler Shift . . . . . . . . . . . . . . . . . . . . . 1246.6.1 Non-relativistic Doppler Shift Review . . . . . . . . . . 1246.6.2 Relativistic Doppler Shift . . . . . . . . . . . . . . . . 1246.7 Relativistic Energy and Momentum . . . . . . . . . . . . . . . 1276.7.1 Relativistic Energy Momentum Conservation . . . . . . 1276.7.2 Relativistic Inertia . . . . . . . . . . . . . . . . . . . . 1286.7.3 Relativistic Energy . . . . . . . . . . . . . . . . . . . . 1296.7.4 Relativistic Three-Momentum . . . . . . . . . . . . . . 1296.7.5 Relationship Between Relativistic Energy and Momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.7.6 Kinetic energy: . . . . . . . . . . . . . . . . . . . . . . 1306.7.7 Massless particles . . . . . . . . . . . . . . . . . . . . 1316.8 Space-time Vectors . . . . . . . . . . . . . . . . . . . . . . . . 1336.8.1 Position Four-Vector: . . . . . . . . . . . . . . . . . . . 1346.8.2 Four-momentum: . . . . . . . . . . . . . . . . . . . . . 1356.8.3 Null four-vectors . . . . . . . . . . . . . . . . . . . . . 1376.8.4 Relativistic Scattering . . . . . . . . . . . . . . . . . . 1376.8.5 More Examples . . . . . . . . . . . . . . . . . . . . . . 1386.9 Relativistic Units . . . . . . . . . . . . . . . . . . . . . . . . . 1396.10 Symmetry Redux . . . . . . . . . . . . . . . . . . . . . . . . . 1406.10.1 Matrix form of Lorentz Transformations . . . . . . . . 1406.10.2 Lorentz Transformations as a Symmetry Group . . . . 1426.11 Supplementary: Four vectors and tensors in covariant form . . 1437 General Relativity 1497.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1497.2 Problems with Newtonian Gravity . . . . . . . . . . . . . . . . 1497.2.1 Review of Newtonian Gravity . . . . . . . . . . . . . . 1497.2.2 Perihelion Shift of Mercury . . . . . . . . . . . . . . . 1517.2.3 Action at a Distance . . . . . . . . . . . . . . . . . . . 1527.2.4 The Puzzle of Inertial vs Gravitational Mass . . . . . . 1537.3 Einstein's Thinking: the Strong Principle of Equivalence . . . 1537.4 Geometry of Spacetime . . . . . . . . . . . . . . . . . . . . . . 1557.5 Some Consequences of General Relativity: . . . . . . . . . . . 1587.6 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . 1597.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1597.6.2 Detection . . . . . . . . . . . . . . . . . . . . . . . . . 1607.6.3 Recent Observations . . . . . . . . . . . . . . . . . . . 1617.7 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.2 Properties: . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.3 Observational Evidence . . . . . . . . . . . . . . . . . . 1647.7.4 Further Information . . . . . . . . . . . . . . . . . . . 1667.8 Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1668 Introduction to the Quantum 1708.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1708.2 Light as particles . . . . . . . . . . . . . . . . . . . . . . . . . 1718.2.1 Review: Light as Waves . . . . . . . . . . . . . . . . . 1718.2.2 Photoelectric Eect . . . . . . . . . . . . . . . . . . . . 1718.2.3 Compton Scattering . . . . . . . . . . . . . . . . . . . 1758.3 Blackbody Radiation and the Ultraviolet Catastrophe . . . . . 1798.3.1 Blackbody Radiation . . . . . . . . . . . . . . . . . . . 1798.3.2 Derivation of Rayleigh-Jeans Law . . . . . . . . . . . . 1818.3.3 The ultraviolet catastrophe . . . . . . . . . . . . . . . 1888.3.4 Quantum resolution: . . . . . . . . . . . . . . . . . . . 1898.3.5 The Early Universe: the ultimate blackbody . . . . . . 1918.4 Particles as waves . . . . . . . . . . . . . . . . . . . . . . . . . 1968.4.1 Electron waves . . . . . . . . . . . . . . . . . . . . . . 1968.4.2 de Broglie Wavelength . . . . . . . . . . . . . . . . . . 1978.4.3 Observational Evidence . . . . . . . . . . . . . . . . . . 1998.5 The Heisenberg Uncertainty Principle . . . . . . . . . . . . . . 2029 The Wave Function 2049.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 2049.2 Quantum vs Newtonian description of physical states . . . . . 2049.2.1 Newtonian description of the state of a particle . . . . 2059.2.2 Quantum description of the state of a particle . . . . . 2059.3 Physical Consequences and Interpretation . . . . . . . . . . . 2079.4 Measurements of position . . . . . . . . . . . . . . . . . . . . 2089.5 Example: Gaussian wavefunction . . . . . . . . . . . . . . . . 2099.6 \Spooky" Action at a Distance: Non-Locality in QuantumMechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2119.6.1 The EPR \Paradox" . . . . . . . . . . . . . . . . . . . 2119.6.2 Bell's Theorem and the Experimental Repudiation ofEPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21410 The Schrodinger Equation 21710.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 21710.2 Momentum in Quantum Mechanics . . . . . . . . . . . . . . . 21810.2.1 Pure Waves . . . . . . . . . . . . . . . . . . . . . . . . 21810.2.2 The Momentum Operator . . . . . . . . . . . . . . . . 22010.3 Energy in Quantum Mechanics . . . . . . . . . . . . . . . . . 22310.4 The Time Independent Schrodinger Equation . . . . . . . . . 22410.4.1 Stationary States . . . . . . . . . . . . . . . . . . . . . 22410.4.2 The \Quantum" in Quantum Mechanics . . . . . . . . 22610.5 Examples of Stationary States . . . . . . . . . . . . . . . . . . 22610.5.1 Free particle in one dimension . . . . . . . . . . . . . . 22610.5.2 Example 2: Particle in a Box with Impenetrable Walls 22710.5.3 Example 3 : Simple Harmonic Oscillator . . . . . . . . 22910.6 Absorption and emission . . . . . . . . . . . . . . . . . . . . . 23110.7 Tunnelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23310.7.1 Tunnelling through a potential barrier of nite width . 23310.7.2 Particle in a Box with Penetrable Walls . . . . . . . . . 23510.7.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 23710.7.4 Applications of tunnelling . . . . . . . . . . . . . . . . 23810.8 The Quantum Correspondence Principle . . . . . . . . . . . . 24210.8.1 Recovering the everyday world . . . . . . . . . . . . . . 24210.8.2 The Bohr Correspondence Principle . . . . . . . . . . . 24310.9 The Time Dependent Schrodinger equation . . . . . . . . . . . 24410.9.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 24611 The Hydrogen Atom 24911.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 24911.2 Newtonian (Classical) Dynamics . . . . . . . . . . . . . . . . . 24911.3 The Bohr Atom . . . . . . . . . . . . . . . . . . . . . . . . . . 25111.4 Semi-classical spectrum from the Bohr correspondence principle25411.5 Emission and Absorption Spectra . . . . . . . . . . . . . . . . 25411.6 Three Dimensional Hydrogen Atom . . . . . . . . . . . . . . . 25611.6.1 Schrodinger Equation . . . . . . . . . . . . . . . . . . . 25611.6.2 Solutions and Quantum Numbers . . . . . . . . . . . . 25811.6.3 Fermions and the spin quantum number . . . . . . . . 26211.7 Periodic Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 26511.7.1 Hydrogen-like atoms . . . . . . . . . . . . . . . . . . . 26511.7.2 Chemical Properties and the Periodic Table . . . . . . 26612 Nuclear Physics 27012.1 Properties of the Nucleus . . . . . . . . . . . . . . . . . . . . . 27012.1.1 Mass of Nucleons . . . . . . . . . . . . . . . . . . . . . 27012.1.2 Structure of Nucleus . . . . . . . . . . . . . . . . . . . 27112.1.3 The Nuclear Force . . . . . . . . . . . . . . . . . . . . 27112.2 Binding Energy and Stability . . . . . . . . . . . . . . . . . . 27412.2.1 Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . 27412.2.2 Binding Energy . . . . . . . . . . . . . . . . . . . . . . 27512.2.3 Binding Energy per Nucleon . . . . . . . . . . . . . . . 27512.3 Formation of Elements: A Brief History of the Universe . . . . 27612.4 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 27912.4.1 Unstable Isotopes . . . . . . . . . . . . . . . . . . . . . 27912.4.2 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . 28112.4.3 Beta decay . . . . . . . . . . . . . . . . . . . . . . . . . 28212.4.4 Alpha Decay . . . . . . . . . . . . . . . . . . . . . . . 28312.4.5 Decay Rates . . . . . . . . . . . . . . . . . . . . . . . . 28312.4.6 Carbon Dating . . . . . . . . . . . . . . . . . . . . . . 28513 Supplementary: Advanced Topics 28713.1 Quantum Information and Quantum Computation . . . . . . . 28713.2 Relativity and quantum mechanics . . . . . . . . . . . . . . . 28714 Conclusions 28815 Appendix: Mathematical Background 28915.1 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . 28915.2 Probabilities and expectation values . . . . . . . . . . . . . . . 29115.2.1 Discrete Distributions . . . . . . . . . . . . . . . . . . 29115.2.2 Continuous probability distributions . . . . . . . . . . 29215.2.3 Dirac Delta Function . . . . . . . . . . . . . . . . . . . 29615.3 Supplementary: Fourier Series and Transforms . . . . . . . . . 29815.3.1 Fourier series . . . . . . . . . . . . . . . . . . . . . . . 29815.3.2 Fourier Transforms . . . . . . . . . . . . . . . . . . . . 30015.3.3 The mathematical uncertainty principle . . . . . . . . . 30215.3.4 Dirac Delta Function Revisited . . . . . . . . . . . . . 30315.3.5 Parseval's Theorem . . . . . . . . . . . . . . . . . . . . 30315.4 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30415.4.1 Moving pure waves . . . . . . . . . . . . . . . . . . . . 30415.4.2 Complex Waves . . . . . . . . . . . . . . . . . . . . . . 30515.4.3 Group velocity and phase velocity . . . . . . . . . . . 30515.4.4 Wave packets . . . . . . . . . . . . . . . . . . . . . . . 30715.4.5 Wave number and momentum . . . . . . . . . . . . . . 30915.5 Derivation of Hydrogen Wave Functions . . . . . . . . . . . . 312
£62.99
Springer Nature Switzerland AG Modern Physics: Introduction to Statistical
Book SynopsisThis book offers an introduction to statistical mechanics, special relativity, and quantum physics. It is based on the lecture notes prepared for the one-semester course of "Quantum Physics" belonging to the Bachelor of Science in Material Sciences at the University of Padova.The first chapter briefly reviews the ideas of classical statistical mechanics introduced by James Clerk Maxwell, Ludwig Boltzmann, Willard Gibbs, and others. The second chapter is devoted to the special relativity of Albert Einstein. In the third chapter, it is historically analyzed the quantization of light due to Max Planck and Albert Einstein, while the fourth chapter discusses the Niels Bohr quantization of the energy levels and the electromagnetic transitions. The fifth chapter investigates the Schrodinger equation, which was obtained by Erwin Schrodinger from the idea of Louis De Broglie to associate to each particle a quantum wavelength. Chapter Six describes the basic axioms of quantum mechanics, which were formulated in the seminal books of Paul Dirac and John von Neumann. In chapter seven, there are several important application of quantum mechanics: the quantum particle in a box, the quantum particle in the harmonic potential, the quantum tunneling, the stationary perturbation theory, and the time-dependent perturbation theory. Chapter Eight is devoted to the study of quantum atomic physics with special emphasis on the spin of the electron, which needs the Dirac equation for a rigorous theoretical justification. In the ninth chapter, it is explained the quantum mechanics of many identical particles at zero temperature, while in Chapter Ten the discussion is extended to many quantum particles at finite temperature by introducing and using the quantum statistical mechanics. The four appendices on Dirac delta function, complex numbers, Fourier transform, and differential equations are a useful mathematical aid for the reader.Table of ContentsTable of Contents1 Classical Statistical Mechanics1.1 Kinetic Theory of Gases 1.1.1 Maxwell Distribution of Velocities1.1.2 Maxwell-Boltzmann Distribution of Energies 1.1.3 Single-Particle Density of States 1.2 Statistical Ensembles of Gibbs 1.2.1 Microcanonical Ensemble 1.2.2 Canonical Ensemble 1.2.3 Grand Canonical Ensemble 1.2.4 Many-Particle Density of States 2 Special Relativity 2.1 Lorentz Transformations 2.2 Einstein Postulates 2.2.1 Gedanken Experiment of Einstein 2.3 Relativistic Mechanics 2.3.1 Relativistic Kinematics 2.3.2 Relativistic Dynamics 3 Quantum Properties of Light 3.1 Black-Body Radiation 3.1.1 Ideal Black Body 3.1.2 Derivation of the Planck Law 3.2 Photoelectric E ect 3.2.1 Experimental Data 3.2.2 Theoretical Explanation 3.3 Energy and Linear Momentum of a Photon 3.4 Compton E ect 3.4.1 Theoretical Explanation 4 Quantum Energy Levels of Atoms 4.1 Energy Spectra 4.1.1 Energy Spectrum of Hydrogen Atom 4.2 Hydrogen Atom of Bohr4.2.1 Derivation of the Bohr Results 4.3 Energy Levels and Photons 4.4 Electromagnetic Transitions 5 Wave Properties of Matter 5.1 De Broglie Wavelength 5.1.1 Explaining the Bohr Quantization 5.2 Experiment of Davisson and Germer 5.3 Double-Slit Experiment with Light5.4 Double-Slit Experiment with Electrons 5.5 Old Quantum Mechanics of Bohr, Wilson and Sommerfeld5.6 Matrix Quantum Mechanics of Heisenberg, Born and Jordan 5.7 Wave Quantum Mechanics of Schrodinger 5.7.1 Derivation of the Schr odinger Equation 5.8 Formal Quantization Rules5.8.1 Schrodinger Equation for a Free Particle 5.8.2 Schrodinger Equation for a Particle in an External Potential 5.9 Stationary Schr odinger Equation6 Axioms of Quantum Mechanics 6.1 Matrix Mechanics 6.2 Axioms of Quantum Mechanics7 Applications of Quantum Mechanics 7.1 Quantum Particle in a One-Dimensional Box Potential7.2 Quantum Particle in a One-Dimensional Harmonic Potential8 Quantum Physics of Atoms 8.1 Quantum Particle in a Separable Potential 8.1.1 Quantum Particle in the Harmonic Potential 8.2 Dirac Notation for a Quantum State8.3 Electron in the Hydrogen Atom 8.3.1 Schrodinger Equation in Spherical Polar Coordinates 8.3.2 Selection Rules 8.4 Pauli Exclusion Principle and the Spin8.5 Semi-Integer and Integer Spin: Fermions and Bosons8.6 The Dirac Equation 8.6.1 The Pauli Equation and the Spin8.6.2 Dirac Equation with a Central Potential 8.6.3 Relativistic Hydrogen Atom and Fine Splitting 8.6.4 Relativistic Corrections to the Schrodinger Hamiltonian9 Quantum Mechanics of Many-Body Systems 9.1 Identical Quantum Particles 9.1.1 Spin-Statistics Theorem9.2 Non-Interacting Identical Particles9.2.1 Atomic Shell Structure and the Periodic Table of the Elements 9.3 Interacting Identical Particles9.3.1 Variational Principle9.3.2 Electrons in Atoms and Molecules10 Quantum Statistical Mechanics 10.1 Quantum Statistical Ensembles 10.1.1 Quantum Microcanonical Ensemble 10.1.2 Quantum Canonical Ensemble 10.1.3 Quantum Grand Canonical Ensemble 10.2 Bosons and Fermions at Finite Temperature 10.2.1 Gas of Photons at Thermal Equlibrium10.2.2 Gas of Massive Bosons at Thermal Equlibrium 10.2.3 Gas of Non-Interacting Fermions at Zero TemperatureAppendix A Dirac Delta Function A.1 The Heaviside Step Function A.2 The Strange Function of Dirac A.2.1 Dirac Function and the Integrals A.3 Dirac Function in D Spatial Dimensions Appendix B Complex Numbers B.1 Set of Complex Numbers B.2 Gauss Plane B.2.1 Polar Representation B.3 Euler Formula B.3.1 Proof of the Euler Formula B.3.2 De Moivre FormulaB.4 Fundamental Theorem of Algebra B.5 Complex Functions Appendix C Fourier Transform C.1 Geometric and Taylor SeriesC.2 Fourier Series .C.2.1 Complex Representation of the Fourier Series C.3 Fourier Integral C.3.1 Properties of the Fourier Transform C.3.2 Fourier Transform and Uncertanty TheoremC.4 Fourier Transform of Space-Time FunctionsAppendix D Di erential equations D.1 First-Order Ordinary Di erential EquationsD.1.1 Separation of Variables D.2 Second-Order Ordinary Di erential Equations D.3 Newton Law as a Second-Order ODE D.4 Partial Di erential Equations D.4.1 Wave Equation D.4.2 Di usion Equation Bibliography
£22.99
Springer Nature Switzerland AG Applications of General Relativity: With Problems
Book SynopsisThe aim of this textbook is to present in a comprehensive way several advanced topics of general relativity, including gravitational waves, tests of general relativity, time delay, spinors in curved spacetime, Hawking radiation, and geodetic precession to mention a few. These are all important topics in today's research activities from both a theoretical and experimental point of view. This textbook is designed for advanced undergraduate and graduate students to strengthen the knowledge acquired during the core courses on General Relativity. The author developed the book from a series of yearly lectures with the intention of offering a gentle introduction to the field. This book helps understanding the more specialized literature and can be used as a first reading to get quickly into the field when starting research. Chapter-end exercises complete the learning material to master key concepts.Trade Review“It is not a textbook, but rather a compendium of, as the title says, applications of General Relativity (GR) … useful for someone who knows the material but wants to look something up, refresh their memory, etc. … The breadth of topics covered is thus smaller than in some other books, but the depth is great. … it is very specialized, but fills an interesting niche.” (Phillip Helbig, The Observatory, Vol. 142 (1291), December, 2022)Table of ContentsIntroduction.- Elements of General Relativity.- Gravitational Waves.- Black Holes.- Tests of General Relativity.- Solutions.
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Springer International Publishing AG Modified and Quantum Gravity: From Theory to
Book SynopsisThis book discusses theoretical predictions and their comparison with experiments of extended and modified classical and quantum theories of gravity. The goal is to provide a readable access and broad overview over different approaches to the topic to graduate and PhD students as well as to young researchers. The book presents both, theoretical and experimental insights and is structured in three parts. The first addresses the theoretical models beyond special and general relativity such as string theory, Poincare gauge theory and teleparallelism as well as Finsler gravity. In turn, the second part is focused on the observational effects that these models generate, accounting for tests and comparisons which can be made on all possible scales: from the universe as a whole via binary systems, stars, black holes, satellite experiments, down to laboratory experiments at micrometer and smaller scales. The last part of this book is dedicated to quantum systems and gravity, showing tests of classical gravity with quantum systems, and coupling of quantum matter and gravity.Table of ContentsPart 1: Theoretical Models beyond special and general relativity Section 1: Aspects of Lorentz invariance violations (Authors: Nick Mavromatos, Luci Menendez-Pidal De Cristina) Section 2: Deformed relativistic symmetry principles (Authors: Giulia Gubitosi, Michele Arzano, Javier Relancio) Section 3: Modified gravity - Poincare gauge theory and teleparallelism (Authors: Yuri Obukhov, Manuel Hohmann) Section 4: Aspects of Finsler gravity and modified dispersion relations in theory and observation (Authors: Volker Perlick, Jean-Francois Gliecenstein) Part 2: Observational effects beyond special and general relativity Section 1: Cosmic searches for Lorentz invariance violations (Authors: Tomislav Terzic, Carloes de los Heros) Section 2: Compact Objects (Authors: Jutta Kunz, Elisa Maggio, Yakov Shnir, Carlos Herdeiro, Aneta Wojnar) Section 3: Testing classical gravity (Authors: Eva Hackmann, Lijing Shao, Sven Herrmann) Section 4: Testing gravity and the standard model at short distance: The Casimir effect (Authors: Galina L. Klimchitskaya, Vladimir Mostepanenko)Part 3: Quantum Systems and Gravity Section 1: Testing Classical Gravity with Quantum Systems (Authors: Sven Herrmann) Section 2: Quantum Gravity in the Lab (Authors: Dennis Raetzel, Annupam Mazumdar, Hendrik Ulbricht) Section 3: Coupling Quantum Matter and Gravity (Authors: Andre Grossardt, Jan-Willem van Holten, Philip Schwartz , Domenico Giulini)
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Springer International Publishing AG Facts of Matter and Light: Ten Physics
Book Synopsis. The main aim of this book is to shine a spotlight on key experiments and their crucial importance for advancing our understanding of physics. Physics is an empirical science, and experiments have always been a driving force in the development of our understanding of nature. Facts matter. In that sense, the book attempts to be complementary to the many popularizations of theoretical physics, and to counterbalance the frequent emphasis there on more speculative ideas.Experimental physics is also an essential pillar in physics teaching, as well as helping broader audiences to better understand important concepts, particularly in challenging fields such as relativity or quantum physics, where our common sense intuition often fails.Readers are taken on an historical journey, starting with “Free Fall” and culminating in “Spooky Action at a Distance”. En route they will encounter many important branches of physics, whose main ideas and theoretical description will be given a more empirical meaning. At the end, the reader is invited to reflect on what could be exciting and important directions for fundamental physics. All readers with an undergraduate degree in physical sciences or engineering will enjoy and learn much from this stimulating and original text.Table of Contents1 The Winners Are . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Free Fall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Equality of Gravitational and Inertial Mass . . . . . . . . . . . . . . . . . . . . . 82.2 Galileo’s Experiments on Free Fall . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Newton’s Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.1 Looking up at the Sky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Newton’s Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4 Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Electromagnetic and Optical Unification . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1 Electromagnetic Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3 The Field Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4 Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.5 Unification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 Looking at Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.1 Natural Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2 Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.3 Limit theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.4 Brownian Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.4.1 The Random Walk as a Diffusion Model . . . . . . . . . . . . . . . . . 394.4.2 Sutherland–Einstein Relation . . . . . . . . . . . . . . . . . . . . . . . . . . 414.5 Perrin’s Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.6 Fluctuation–Dissipation Relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.1 Standard Hydrogen Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.2 Black Body Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.3 Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54xixii Contents5.4 Compton Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.5 Specific Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.6 Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636 Wave-like Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.1 Early light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.1.1 Young’s Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.1.2 On the French side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.1.3 Interacting Newton Bullets? . . . . . . . . . . . . . . . . . . . . . . . . . . . 736.2 X-rays and Bragg Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.3 Davisson–Germer Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.4 Wavy Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807 Finding Structure: Scattering and Fission . . . . . . . . . . . . . . . . . . . . . . . . . 857.1 Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.2 Particle Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887.2.1 Geiger–Marsden–Rutherford Scattering . . . . . . . . . . . . . . . . . . 887.2.2 Standard Model Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 937.3 Nuclear Chain Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 948 Light in the Universe and the Invariance of Proper Time . . . . . . . . . . . 978.1 Michelson–Morley Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 988.2 Special Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1018.2.1 Popular Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1028.2.2 Minkowski Spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1038.2.3 Twin Paradox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1058.2.4 NonEuclidean Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1068.3 And More Generally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1069 Dynamical Activity of the Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1099.1 Beginnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1109.2 Lamb Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1129.2.1 Lamb–Retherford Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . 1129.2.2 Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1159.3 Fluctuation Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1169.4 Casimir Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1179.5 Frenesy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11810 Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12110.1 The Dream of Anaximenes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12310.2 Percolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12410.3 Criticality and Universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12710.4 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13110.5 Superfluidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13210.6 Bose–Einstein Condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Contents xiii11 Nonlocality: Spooky Action at a Distance . . . . . . . . . . . . . . . . . . . . . . . . . 13511.1 About Alice, Living Far away from Bob . . . . . . . . . . . . . . . . . . . . . . . . 13711.2 Einstein’s Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13911.3 Einstein–Podolsky–Rosen Argument . . . . . . . . . . . . . . . . . . . . . . . . . . 14011.4 Bell’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14211.5 Bell Test Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14412 Future Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14712.1 Around 2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14812.1.1 The Statistical Mechanics of Geometry . . . . . . . . . . . . . . . . . . 15112.1.2 Relativity versus Quantum Mechanics . . . . . . . . . . . . . . . . . . . 15212.1.3 Quantum Statistical Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . 15312.2 Into the next hundred years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15512.2.1 Computational and Neuro(nal) Physics . . . . . . . . . . . . . . . . . . 15512.2.2 Physics of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15712.2.3 Many-Body Nonequilibrium Physics . . . . . . . . . . . . . . . . . . . . 15912.2.4 Climate and Planetary Sciences . . . . . . . . . . . . . . . . . . . . . . . . 160References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
£58.49
Springer International Publishing AG Special Relativity
Book SynopsisThis book offers an essential bridge between college-level introductions and advanced graduate-level books on special relativity. It begins at an elementary level, presenting and discussing the basic concepts normally covered in college-level works, including the Lorentz transformation. Subsequent chapters introduce the four-dimensional worldview implied by the Lorentz transformations, mixing time and space coordinates, before continuing on to the formalism of tensors, a topic usually avoided in lower-level courses. The book’s second half addresses a number of essential points, including the concept of causality; the equivalence between mass and energy, including applications; relativistic optics; and measurements and matter in Minkowski space-time. The closing chapters focus on the energy-momentum tensor of a continuous distribution of mass-energy and its co-variant conservation; angular momentum; a discussion of the scalar field of perfect fluids and the Maxwell field; and general coordinates.Every chapter is supplemented by a section with numerous exercises, allowing readers to practice the theory. These exercises constitute an essential part of the textbook, and the solutions to approximately half of them are provided in the appendix.Trade ReviewFrom the reviews:“The book is one of the best texts in special relativity designed for readers between the college-level and advanced level. … A number of useful and new examples is added at the end of every chapter of the book. … A very useful table of constants is added at the end of the book. … The book represents one of the best conspects in special relativity and is useful for professors of special relativity. It is good for students and every other reader.” (Alex Gaina, zbMATH, Vol. 1277, 2014)Table of ContentsFundamentals of Special Relativity.- Introduction.- The Principle of Relativity.- Groups—the Galilei group.- Galileian law of addition of velocities.- The lesson from electromagnetism.- The postulates of Special Relativity.- Consequences of the postulates.- Conclusion.- Problems.- The Lorentz transformation.- Introduction.- The Lorentz transformation.- Derivation of the Lorentz transformation.- Mathematical properties of the Lorentz transformation.- Absolute speed limit and causality.- Length contraction from the Lorentz transformation.- Time dilation from the Lorentz transformation.- Transformation of velocities and accelerations in Special Relativity.- Matrix representation of the Lorentz transformation.- The Lorentz group.- The Lorentz transformation as a rotation by an imaginary angle with imaginary time.- The GPS system.- Conclusion.- Problems.- The 4-dimensional world view.- Introduction.- The 4-dimensional world.- Spacetime diagrams.- Conclusion.- Problems.- The formalism of tensors.- Introduction.- Vectors and tensors.- Contravariant and covariant vectors.- Contravariant and covariant tensors.- Tensor algebra.- Tensor fields.- Index-free description of tensors.- The metric tensor.- The Levi-Civita symbol and tensor densities.- Conclusion.- Problems.- Tensors in Minkowski spacetime.- Introduction.- Vectors and tensors in Minkowski spacetime.- The Minkowski metric.- Scalar product and length of a vector in Minkowski spacetime.- Raising and lowering tensor indices.- Causal nature of 4-vectors.- Hypersurfaces.- Gauss’ theorem.- Conclusion.- Problems.- Relativistic mechanics.- Introduction.- Relativistic dynamics of massive particles.- The relativistic force.- Angular momentum of a particle.- Particle systems.- Conservation of mass-energy.- Conclusion.- Problems.- Relativistic optics.- Introduction.- Relativistic optics: null rays.- The drag effect.- The Doppler effect.- Aberration.- Relativistic beaming.- Visual appearance of extended objects.- Conclusion.- Problems.- Measurements in Minkowski spacetime.- Introduction.- Energy of a particle measured by an observer.- Frequency measured by an observer.- A more systematic treatment of measurement.- The 3+1 splitting.- Conclusion.- Problems.- Matter in Minkowski spacetime.- Introduction.- The energy-momentum tensor.- Covariant conservation.- Energy conditions.- Angular momentum.- Perfect fluids.- The scalar field.- The electromagnetic field.- Conclusion.- Problems.- Special Relativity in arbitrary coordinates.- Introduction.- The covariant derivative.- Spacetime curves and covariant derivative.- Physics in Minkowski spacetime revisited.- Conclusions.- Problems.- Solutions to selected problems.- References.- Index.
£22.99
Springer International Publishing AG Quantum Aspects of Black Holes
Book SynopsisBeginning with an overview of the theory of black holes by the editor, this book presents a collection of ten chapters by leading physicists dealing with the variety of quantum mechanical and quantum gravitational effects pertinent to black holes. The contributions address topics such as Hawking radiation, the thermodynamics of black holes, the information paradox and firewalls, Monsters, primordial black holes, self-gravitating Bose-Einstein condensates, the formation of small black holes in high energetic collisions of particles, minimal length effects in black holes and small black holes at the Large Hadron Collider. Viewed as a whole the collection provides stimulating reading for researchers and graduate students seeking a summary of the quantum features of black holes.Table of ContentsFundamental Physics with Black Holes (Xavier Calmet).- Black holes and thermodynamics - The first half century (Daniel Grumiller, Robert McNees and Jakob Salzer).- The Firewall Phenomenon (R. B. Mann).- Monsters, Black holes and Entropy (Stephen D. H. Hsu).- Primordial Black Holes: sirens of the early Universe (Anne M. Green).- Self-gravitating Bose-Einstein condensates (Pierre-Henri Chavanis).- Quantum Amplitudes in Black-Hole Evaporation with Local Supersymmetry (P.D.D'Eath and A.N.St.J.Farley).- Hawking radiation from higher-dimensional black holes (Panagiota Kanti and Elizabeth Winstanley).- Black Holes at the Large Hadron Collider (Greg Landsberg).- Minimum length effects in black hole physics (Roberto Casadio, Octavian Micu, Piero Nicolini).
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Der Schwerkraft auf der Spur
Book SynopsisIn diesem Buch wird der Versuch unternommen, Schülern der oberen Klassen und allen, die sich für Physik inter essieren, etwas über die Gravitation zu vermitteln. Durch die gravitative Wechselwirkung-die schwächste aller in der Natur bekannten Wechselwirkungen-wird die Bewegung der Himmelskörper, der Planeten, Sterne und Galaxien, sowie die Entwicklung des Universums als Ganzes bestimmt. Unter Laborbedingungen sind die gra vitativen Effekte jedoch so klein, daß es keine leichte Aufgabe ist, sie zu messen. Als die Autoren dieses Buch über die gravitative Wechselwirkung schrieben, bemühten sie sich, dem Aus spruch des sowjetischen Physikers I. Je. Tamm zu folgen: "Ein Student ist keine Gans, die man füllen, sondern eine Fackel, die man anzünden muß." Offensichtlich gilt das auch für Schüler (von denen ja einige später Studenten werden). Daher haben sich die Autoren folgende Aufgabe gestellt: Erstens wollen sie den Leser mit den modernen Vorstellungen über die gravitative Wechselwirkung be kannt machen. Zweitens wollen sie ihn empfinden lassen, wie die erstaunlichen Besonderheiten der Gravitation im Experiment zutage treten. In diesem Buch wird auch ein wenig über die histori sche Entwicklung der Ideen und Experimente berichtet.Table of Contents1. Über das physikalische Experiment im allgemeinen und über die Gravitationsexperimente im besonderen.- 2. Was wußte Newton über die Schwerkraft?.- 3. Die Relativität der Bewegung.- 4. Was besagt die Allgemeine Relativitätstheorie?.- 5. Welche Beobachtungshinweise liefert die Allgemeine Relativitätstheorie?.- 6. Das Meßpotential der Menschheit—gestern und heute.- 7. Wieviele Massesorten gibt es?.- 8. Wie entsteht die Rot- bzw. Violettverschiebung elektromagnetischer Wellen?.- 9. Die Sonne verzerrt das Bild der Metagalaxis und verzögert Radioechos.- 10. Inwiefern irrte Kepler?.- 11. Das Gravitationsfeld rotierender Körper.- 12. Wie kann man Gravitationswellen empfangen?.- 13. Wie „erkennt“ man ein Schwarzes Loch?.- 14. Die Gravitation am Rande der Metagalaxis.- 15. Ist die Gravitationskonstante wirklich konstant? (Über andere Gravitationstheorien).- Schlußwort.- Anhang: Welchen Nutzen besitzt die Gravimetrie, und gibt es Schwerelosigkeit auf der Umlaufbahn?.
£31.34
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Bryce DeWitt's Lectures on Gravitation: Edited by Steven M. Christensen
Book SynopsisBryce DeWitt, a student of Nobel Laureate Julian Schwinger, was himself one of the towering figures in 20th century physics, particularly renowned for his seminal contributions to quantum field theory, numerical relativity and quantum gravity. In late 1971 DeWitt gave a course on gravitation at Stanford University, leaving almost 400 pages of detailed handwritten notes. Written with clarity and authority, and edited by his former student Steven Christensen, these timeless lecture notes, containing material or expositions not found in any other textbooks, are a gem to be discovered or re-discovered by anyone seriously interested in the study of gravitational physics.Trade ReviewFrom the reviews:“DeWitt’s lectures cover interesting and detailed material which is rarely found in other text books. It is a book for the advanced reader.” (Norbert Dragon, General Relativity and Gravitation, Vol. 44, 2012)Table of ContentsReview of the Uses of Invariants in Special Relativity.- Accelerated Motion in Special Relativity.- Realization of Continuous Groups.- Riemannian Manifolds.- The Free Particle Geodesics.- Weak Field Approximation. Newton`s Theory.- Ensembles of Particles.- Production of Gravitational Fields by Matter.- Conservation Laws.- Phenomenological Description of a Conservative Continuous Medium.- Solubility of the Einstein and Matter Equations.- Energy, Momentum and Stress in the Gravitational Field.- Measurement of Asymptotic Field.- The Electromagnetic Field.- Gravitational Waves.- Spinning Bodies.- Weak Field Gravitational Wave.- Stationary Spherically (or Rotationally) Symmetric Metric.- Kerr Metric Subcalculations.- Friedmann Cosmology.- Dynamical Equations and Diffeomorphisms.
£61.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Physics of Black Holes: A Guided Tour
Book SynopsisBlack Holes are still considered to be among the most mysterious and fascinating objects in our universe. Awaiting the era of gravitational astronomy, much progress in theoretical modeling and understanding of classical and quantum black holes has already been achieved. The present volume serves as a tutorial, high-level guided tour through the black-hole landscape: information paradox and blackhole thermodynamics, numerical simulations of black-hole formation and collisions, braneworld scenarios and stability of black holes with respect to perturbations are treated in great detail, as is their possible occurrence at the LHC. An outgrowth of a topical and tutorial summer school, this extensive set of carefully edited notes has been set up with the aim of constituting an advanced-level, multi-authored textbook which meets the needs of both postgraduate students and young researchers in the fields of modern cosmology, astrophysics and (quantum) field theory. Table of ContentsBlack Holes and their Properties.- What Exactly is the Information Paradox?.- Classical Yang–Mills Black Hole Hair in Anti-de Sitter Space.- Black Hole Thermodynamics and Statistical Mechanics.- Colliding Black Holes and Gravitational Waves.- Numerical Simulations of Black Hole Formation.- Higher-Dimensional Black Holes.- Black Holes in Higher-Dimensional Gravity.- Braneworld Black Holes.- Higher Order Gravity Theories and Their Black Hole Solutions.- Gravitational Waves from Braneworld Black Holes.- Black Holes at the Large Hadron Collider.- Perturbations of Black Holes.- Perturbations and Stability of Higher-Dimensional Black Holes.- Analytic Calculation of Quasi-Normal Modes.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG The Physics of the Early Universe
Book SynopsisThe Physics of the Early Universe is an edited and expanded version of the lectures given at a recent summer school of the same name. Its aim is to present an advanced multi-authored textbook that meets the needs of both postgraduate students and young researchers interested in, or already working on, problems in cosmology and general relativity, with emphasis on the early universe. A particularly strong feature of the present work is the constructive-critical approach to the present mainstream theories, the careful assessment of some alternative approaches, and the overall balance between theoretical and observational considerations. As such, this book will also benefit experienced scientists and nonspecialists from related areas of research. Trade ReviewFrom the reviews: "This is a set of 9 review articles given as part of a 2003 summer school on Syros Island, Greece. … this book provides a solid introduction to current research in early universe physics, which should be useful for PhD students or postdoctoral researchers who want the real thing. … This, then, is a useful book for someone wanting to leap right into modern theoretical ideas of early universe physics." (Douglas Scott, Classical and Quantum Gravity, Issue 24, 2007)Table of ContentsAn Introduction to the Physics of the Early Universe.- Cosmological Perturbation Theory.- Cosmic Microwave Backgrond Anisotropies.- Oberservational Cosmology.- Dark Matter and Dark Energy.- String Cosmology.- Brane-World Cosmology.- Gravitational Wave Astronomy: the High Frequency Window.- Computational Black Hole Dynamics.
£40.49
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.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Globular Clusters - Guides to Galaxies:
Book SynopsisThe idea to hold a workshop on globular clusters in Concepcion emerged during 2005 out of a variety of circumstances. Four years had passed since the IAUSymposium 207 onExtragalactic Globular Clusters inPuc' on, atime span, which we thought to be long enough for justifying a new meeting with theintent toreviewthemostrecentdevelopments inthe?eld of extragalactic stars clusters. Originally intended to be a small-scale workshop, the response from the community was overwhelming so that only a full-scale international conferencewas abletocopewith thenumerousrequestsfortalksandposters. Finally, about 160 participants gathered in Concepci' on on March 6th, 2006. The venue was the university lecture hall located in the facultad de - manidadesyartesoftheUniversidaddeConcepci' on.Posterswereexposedin the lobby of the faculty building. The weather was as good as one can reas- ablyexpectfromalatesummerinConcepci' on.Althoughtheprogrammewas so tight that separate poster sessions other than those during co?ee breaks could not be accomodated, posters received a lot of attention. From the ?rst to the last talk, the atmosphere was inspiring and the conference could keep its tension for ?ve full days. This clearly shows that the attraction which globular clusters exercise on astrophysicists of quite di?erent ?avours, is as strong as ever.Table of ContentsDetailed Studies of Individual Globular Clusters.- Detailed Chemical Abundances of Extragalactic Globular Clusters.- Spectroscopic Abundances and Radial Velocities of the Galactic Globular Clusters 2MASS GC01 and 2MASS GC02: Preliminary Results.- Abundance Anomalies in Galactic Globular Clusters – Looking for the Stellar Culprits.- Globular Clusters in the Direction of the Inner Galaxy.- Globular Cluster Research with Astronomical Archives.- Super-He-Rich Populations in Globular Clusters.- Testing the BH 176 and Berkeley 29 Association with GASS/Monoceros.- New Yonsei-Yale (Y 2) Isochrones and Horizontal-Branch Evolutionary Tracks with Helium Enhancements.- Search for Candle Stars in Globular Clusters: Spectroscopic Analysis of Post-AGB Candidates.- The Lack of Binaries Among Hot Horizontal Branch Stars: M80 and NGC5986.- Semi-Empirical Determination of the Mass Distribution of Horizontal Branch Stars in M3.- The Most Massive Clusters.- Globular Clusters, Galactic Nuclei and Supermassive Black Holes.- UCDs – A Mixed Bag of Objects.- Ultra-Compact Dwarf Galaxies and Globular Clusters: A Review of Their Spatial and Dynamical Properties.- The Maximum Mass of Star Clusters.- The Stellar Population of Ultra-Compact Dwarf Galaxies.- News on Ultra-Compact Dwarfs and Blue Globular Clusters.- UCDs and GCs: Structural Differences from HST Imaging.- Ultra-Compact Stellar Systems in the Fornax Galaxy Cluster.- Multi-Colour Imaging of Ultra-Compact Objects in the Fornax Cluster.- Young Star Clusters.- Hierarchical Formation of Galactic Clusters.- Young Massive Clusters – Formation Efficiencies and (Initial) Mass Functions.- The Radii of Thousands of Star Clusters in M51 with HST/ACS.- Extragalactic Star Clusters in Merging Galaxies.- The Environment of Young Massive Clusters.- Star/Cluster Formation in Complexes: Insights from IFUs and HST.- Spectral Evolution of Blue Concentrated Star Clusters in the Large Magellanic Cloud.- Young Star Clusters in the SMC.- Molecular Clouds and Star Formation in the Magellanic System by NANTEN.- Two Star Cluster Populations in NGC 45.- Characterization of Open Cluster Remnants.- HST Photometry of the Binary Globular Cluster Sersic 13N-S in NGC5128[1].- Globular Cluster Systems in Dwarf and Irregular Galaxies.- LMC Cluster Abundances and Kinematics.- Globular Clusters in Dwarf Galaxies.- Globular Clusters in Dwarf and Giant Galaxies.- The Age-Metallicity Relation of the SMC.- Integrated Spectroscopic Analysis of Galactic and Small Magellanic Cloud Clusters.- Variable Stars in the Globular Clusters and in the Field of the Fornax dSph Galaxy.- Physical Parameters of Intermediate-Age LMC Clusters from Modelling of HST CMDs.- RGB Properties of the LMC/SMC Clusters in the Infrared.- WLM-1: A Non-Rotating, Gravitationally Unperturbed, Highly Elliptical Extragalactic Globular Cluster.- Globular Cluster Systems in Spiral Galaxies.- Star Clusters in M33 – Clues to Galaxy Formation and Evolution.- M31 and its Globular Clusters.- IR Integrated Light Colors For Galactic GCs and An Update on Young M31 Globular Clusters.- Nuclear Star Clusters in Edge-on Galaxies.- HST ACS Wide-Field Photometry of the Sombrero Galaxy Globular Cluster System.- Intermediate-Age Globular Clusters in M31.- Metal-Poor Globular Clusters of the Galactic Bulge.- Globular Cluster System and Milky Way Properties Revisited.- RR Lyrae-Based Calibration of the Globular Cluster Luminosity Function.- Globular Cluster Systems in Spiral Galaxies Using ACS Imaging.- Laser Guide Star Imaging of M31 Globulars.- GALEX UV Observations of M31 Globular Clusters.- Integrated Spectroscopy of Galactic Globular Clusters.- Globular Cluster Systems in Early-Type Galaxies.- Globular Cluster Systems: Do They Really Trace Star Formation? (Or Rather: What Mode of Star Formation Do They Trace?).- Globular Clusters in Early Type Galaxies.- Globular Clusters and Galaxy Formation.- Globular Cluster Systems in Giant Ellipticals: New and Old Patterns.- The ACS Virgo Cluster Survey.- Globular Clusters at the Centre of the Fornax Cluster: Tracing Interactions Between Galaxies.- Globular Cluster Bimodality Revisited (and the Globulars-Galaxy Halo Connection).- Globular Cluster Systems, Diffuse Star Clusters, and Host Galaxies in the ACS Virgo Cluster Survey.- Hot Populations in M87 Globular Clusters.- A Subaru/Suprime-Cam Wide-Field Survey of Globular Cluster Populations around M87.- Stellar Populations of Globular Clusters in NGC 1407.- The Globular Cluster System of NGC 5846 Revisited: Colours, Sizes and X-Ray Counterparts.- Globular Cluster Systems in Shell Ellipticals.- GMOS Photometry of Five Globular Cluster Systems: NGC 4649, NGC 3923, NGC 524, NGC 3115 and NGC 3379.- Structural Parameters from Ground-based Observations of Globular Clusters in NGC 5128.- Globular Cluster Populations in Early-Type Galaxies.- The Low-Mass X-Ray Binary Globular Cluster Connection in the ACS Virgo Cluster Survey.- The Globular Cluster System of NGC 5128: Combining Broad-Band Color and Lick Index Analysis.- The Galaxy – Globular Cluster Connection in NGC 3115.- Velocity Dispersions of Bright Globular Clusters in NGC 5128.- Evolution of Cluster Systems and their Host Galaxies.- Imprint of Galaxy Formation and Evolution on Globular Cluster Properties.- Formation of Globular Clusters in Hierarchical Cosmology: ART and Science.- Globular Cluster Formation in Mergers.- The Formation Histories of Metal-Rich and Metal-Poor Globular Clusters.- Globular Cluster System Evolution in Early Type Galaxies.- Star Cluster Evolution: From Young Massive Star Clusters to Old Globulars.- A Wide-Field Survey of the Globular Cluster Systems of Giant Galaxies.- IGCs in the Virgo Cluster.- A New Explanation of Globular Cluster Color Distributions.- Formation of Intracluster and Intercluster Globular Clusters.- The Effect of Giant Molecular Clouds on Star Clusters.- Metal-rich Globular Clusters: An Unaccounted Factor Responsible for Their Formation?.- On the Globular Cluster Color Distributions.- Dynamical Evolution of Star Clusters.- Dissolution of Globular Clusters.- Dynamical Masses of Young Star Clusters: Constraints on the Stellar IMF and Star-Formation Efficiency.- Dynamical Evolution of Rotating Globular Clusters with Embedded Black Holes.- The Dynamical Evolution of Young Clusters and Galactic Implications.- Simulations of Globular Clusters Merging in Galactic Nuclear Regions.- The Origin of the Gaussian Initial Mass Function of Globular Cluster Systems.- Evolution of Globular Cluster Systems.- Tidal Disruption and the Tale of Three Clusters.- Tidal Tails Around Globular Clusters: Are they Good Tracers of Cluster Orbits?.- Modelling the Tidal Tails of NGC 5466.- The Search for Tidal Tails of Globular Clusters: NGC4147.- Internal Rotation of Young Globular Clusters.- Mass Segregation in Young Star Clusters.- Dynamics of Globular Cluster Systems.- Kinematics of Globular Cluster Systems.- Dark Matter in the Elliptical Galaxies NGC 1399 and NGC 4636.- Ages, Abundances, and Kinematics of Globular Clusters in NGC 3379 and NGC 4649 with Gemini/GMOS.- The Dark Halo of NGC 1399 and MOND.- Dynamics of the Globular Cluster System of NGC 5128.- Open Questions in the Globular Cluster – Galaxy Connection.- Open Questions in the Globular Cluster – Galaxy Connection.
£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 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-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 Gesammelte Werke / Collected Works: Volume 2
Book SynopsisDer bekannte Astronom Karl Schwarzschild (1873-1916) gilt als der Begr}nder der Astrophysik und als hervorragender Forscher mit einer erstaunlichen Bandbreite seiner Interessen. Arbeiten zur Himmelsmechanik, Elektrodynamik und Relativit{tstheorie weisen ihn als vorz}glichen Mathematiker und Physiker seiner Zeit aus. Untersuchungen zur Photographischen Photometrie, Optik und Spektroskopie zeigen den versierten Beobachter, der sein Me~instrument beherrscht. Schlie~lich arbeitete Schwarzschild als Astrophysiker und an Sternatmosph{ren, Kometen, Struktur und Dynamikvon Sternsystemen. Die in seinem kurzen Leben entstandene F}lle von wissenschafltichen Arbeiten ist in drei B{nden der Gesamtausgabe gesammelt, erg{nzt durch biographisches Material und ein Essay des Nobelpreistr{gers S. Chandrasekhar und Annotationen von Fachleuten in jedem der drei B{nde.Table of Contents5. Astronomical Positioning.- 5.1 Ueber photographische Ortsbestimmung / On Photographic Position Determination.- 5.2 Über photographische Breitenbestimmung mit Hilfe eines hängenden Zenitkollimators / On Determining Latitude Using a Suspended Zenith Collimator.- 5.3 Über Breitenbestimmung mit Hilfe einer hängenden Zenitkamera / On Latitude Determination Using a Suspended Zenith Camera.- 5.4 Bestimmung der Polhöhe von Göttingen u. der Deklinationen von 375 Zenithsternen mit der hängenden Zenithkamera / Determination of the Altitude of the Pole at Göttingen and the Declination of 375 Zenith Stars Using the Suspended Zenith Camera (with W. Dziewulski).- 5.5 Über einen Transformator zur Auflösung sphärischer Dreiecke, besonders für Zwecke der Ortsbestimmung im Luftballon / On a Transformer for the Solution of Spherical Triangles, Especially for Position Determination in Air Balloons.- 5.6 Tafeln zur astronomischen Ortsbestimmung im Luftballon bei Nacht, sowie zur leichten Bestimmung der mitteleuropäischen Zeit an jedem Orte Deutschlands / Tables for Astronomical Position Determination in Air Balloons at Night and for Easy Determination of Central-European Time at any Point in Germany (with o. Birck).- 5.7 Künstlicher Horizont and Ballonsextant / Artificial Horizon and Balloon Sextant.- 5.8 Libellenhorizont und Libellensextant / Bubble Horizon and Bubble Sextant.- 6. Photographie Photometry.- 6.1 Die Bestimmung von Sternhelligkeiten aus extrafocalen photographischen Aufnahmen / The Determination of Stellar Magnitudes from Extrafocal Exposures.- 6.2 Beiträge zur photo graphischen Photometrie der Gestirne / Contributions on the Photographic Photometry of Stars.- 6.3 Ueber Abweichungen vom Reciprocitätsgesetz für Bromsilbergelatine / On Departures from the Reciprocity Law for Silver-Bromide Gelatine.- 6.4 Ueber die Wirkung intermittirender Belichtung auf Bromsilbergelatine / On the Effects of Intermittent Exposures on Silver-Bromide Gelatine.- 6.5 Bemerkungen zur Sensitometrie / Remarks on Sensitometry.- 6.6 über die photographische Vergleichung der Helligkeit verschiedenfarbiger Sterne / On the Photographic Comparison of the Magnitudes of Stars of Different Colours.- 6.7 Ueber sensitometrische Regeln und ihre astronomische Anwendung / On Sensitometry Laws and Their Astronomical Application.- 6.8 Professor G. Jägers Theorie des photographischen Prozesses / Professor G. Jäger’sf Theory of the Photographic Process.- 6.9 Plan zur Durchführung einer photographisch-photometrischen Durchmusterung des nördlichen Himmels / Plan for Carrying Out a Photographic-Photometric Survey of the Northern Sky.- 6.10 Über eine Schraffierkassette zur Aktinometrie der Sterne / On a Schraffierkassette for Stellar Actinometry (with Br. Meyermann).- 6.11 Über eine Interpolationsaufgabe der Aktinometrie / On an Interpolation Problem in Actinometry.- 6.12 Aufnahmen des Sternhaufens h Persei mit Spiegeln von sehr großem öffnungsverhältnis / Exposures of the Cluster h Persei Using Mirrors with Very Large Aperture Ratios (with W. Villiger).- 6.13 Über eine neue Schraffierkassette / On a New Schraffierkassette (with Br. Meyermann).- 6.14 Über die Farbentönung der Sterne / On the Colour Tints of the Stars.- 6.15 Remarque sur la determination des grandeurs photographiques absolues / Note on the Determination of Absolute Photographic Magnitudes.- 6.16 Über die Bestimmung absoluter photographischer Helligkeiten / On the Determination of Absolute Photographic Magnitudes.- 6.17 Aktinometrie der Sterne der B.D. bis zur Grösse 7.5 in der Zone 0 ° bis + 20 ° Deklination. Teil A / Actinometry of B.D. Stars down to Magnitude 7.5 in the Zone between Declinations 0 ° and + 20 ° , Part A (with Br. Meyermann, A. Kohlschütter and O. Birck).- 6.18 Aktinometrie der Sterne der B.D. bis zur Grösse 7.5 in der Zone 0 ° bis + 20 ° Deklination. Teil B / Actinometry of B.D. Stars down to Magnitude 7.5 in the Zone between Declinations 0 ° and +20 ° , Part B (with Br. Meyermann, A. Kohlschütter, O. Birck and W. Dziewulski).- 6.19 Buchbesprechung / Book Review: J.A. Parkhurst, Yerkes Actinometry, Zone + 73 ° to + 90 °.- 6.20 Über die Schleierkorrektion bei der Halbgittermethode zur Bestimmung photographischer Sterngrößen / On the Correction for Fogging in the Half-Grating Method of Determining Photographic Stellar Magnitudes.- 6.21 Vorbemerkung zu / Introduction to: W. Dziewulski, Photographische Größen von Sternen in der Nähe des Nordpols / Photographic Magnitudes of Stars Near the North Pole.- 7. Measuring Techniques, Binary Stars, Variable Stars and Spectroscopy.- 7.1 Ueber Messung von Doppelsternen durch Interferenzen / On Measuring Double Stars by Interference Methods.- 7.2 Zur Bestimmung der Theilungsfehler von Maassstäben / On Determining Dividing Errors of Graduated Scales.- 7.3 Beitrag zur Bestimmung von Radialgeschwindigkeiten mit dem Objektivprisma / Contribution on the Determination of Radial Velocities with an Objective Prism.- 7.4 Einige Beobachtungen der Radialgeschwindigkeit von 0: Coronae borealis mit dem Objektivprisma / Some Observations of the Radial Velocity of 0: Coronae borealis with an Objective Prism.- 7.5 über die Radialgeschwindigkeit des Sterns 63 Tauri / On the Radial Velocity of the Star 63 Tauri.- 7.6 Präzisionstechnik und wissenschaftliche Forschung / Precision Engineering and Scientific Research.- 7.7 Spectral Classification of Stars (in German).- 7.8 Ein Verfahren der Bahnbestimmung bei spectroskopischen Doppelsternen / A Procedure for Deterrnining the Orbits of Spectroscopic Binaries.- 7.9 Beobachtungen von Veränderlichen Sternen und der Nova Aurigae / Observations of Variable Stars and of Nova Aurigae.- 7.10 Ein neuer Veränderlicher (41.1910 Tauri) in den Hyaden / A New Variable (41.1910 Tauri) in the Hyades.- 7.11 über den Lichtwechsel des Veränderlichen 41.1910 Tauri / On the Variations in Brightness of the Variable 41.1910 Tauri.- 7.12 Nova 18.1912 Geminorum (Bemerkung zum Spektrum der Eneboschen Nova) /Nova 18.1912 Geminorum (Remark on the Spectrum of Enebo’s Nova).- 7.13 Der neue Stern in den Zwillingen / The New Star in the Constellation Gemini.- for Volume 1.- for Volume 3.
£119.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Physics of Gravitating Systems I: Equilibrium and Stability
Book SynopsisIt would seem that any specialist in plasma physics studying a medium in which the interaction between particles is as distance-dependent as the inter action between stars and other gravitating masses would assert that the role of collective effects in the dynamics of gravitating systems must be decisive. However, among astronomers this point of view has been recog nized only very recently. So, comparatively recently, serious consideration has been devoted to theories of galactic spiral structure in which the dominant role is played by the orbital properties of individual stars rather than collec tive effects. In this connection we would like to draw the reader's attention to a difference in the scientific traditions of plasma physicists and astrono mers, whereby the former have explained the delay of the onset of controlled thermonuclear fusion by the "intrigues" of collective processes in the plasma, while many a generation of astronomers were calculating star motions, solar and lunar eclipses, and a number of other fine effects for many years ahead by making excellent use of only the laws of Newtonian mechanics. Therefore, for an astronomer, it is perhaps not easy to agree with the fact that the evolution of stellar systems is controlled mainly by collective effects, and the habitual methods of theoretical mechanics III astronomy must make way for the method of self-consistent fields.Table of Contents(Volume I).- § 1. Basic Concepts and Equations of Theory.- § 2. Equilibrium States of Collisionless Gravitating Systems.- § 3. Small Oscillations and Stability.- §4. Jeans Instability of a One—Component Uniform Medium.- §5. Jeans Instability of a Multicomponent Uniform Medium.- 5.1. Basic Theorem (on the Stability of a Multicomponent System with Components at Rest).- 5.2. Four Limiting Cases for a Two—Component Medium.- 5.3. Table of Jeans Instabilities of a Uniform Two—Component Medium.- 5.4. General Case of n Components.- §6. Non—Jeans Instabilities.- § 7. Qualitative Discussion of the Stability of Spherical, Cylindrical (and Disk—Shaped) Systems with Respect to Radial Perturbations.- I Theory.- I Equilibrium and Stability of a Nonrotating Flat Gravitating Layer.- § 1. Equilibrium States of a Collisionless Flat Layer.- § 2. Gravitational (Jeans) Instability of the Layer.- § 3. Anisotropic (Fire—Hose) Instability of a Collisionless Flat Layer.- 3.1. Qualitative Considerations.- 3.2. Derivation of the Dispersion Equation for Bending Perturbations of a Thin Layer.- 3.3. Fire—Hose Instability of a Highly Anisotropic Flat Layer.- 3.4. Analysis of the Dispersion Equation.- 3.5. Additional Remarks.- § 4. Derivation of Integra—Differential Equations for Normal Modes of a Flat Gravitating Layer.- § 5. Symmetrical Perturbations of a Flat Layer with an Isotropic Distribution Function Near the Stability Boundary.- § 6. Perpendicular Oscillations of a Homogeneous Collisionless Layer.- 6.1. Derivation of the Characteristic Equation for Eigenfrequencies.- 6.2. Stability of the Model.- 6.3. Permutational Modes.- 6.4. Time—Independent Perturbations (? = 0).- Problems.- II Equilibrium and Stability of a Collisionless Cylinder.- §1. Equilibrium Cylindrical Configurations.- § 2. Jeans Instability of a Cylinder with Finite Radius.- 2.1. Dispersion Equation for Eigenfrequencies of Axial-Symmetrical Perturbations of a Cylinder with Circular Orbits of Particles.- 2.2. Branches of Axial—Symmetrical Oscillations of a Rotating Cylinder with Maxwellian Distribution of Particles in.- 2.3. Longitudinal Velocities.- 2.4. Oscillative Branches of the Rotating Cylinder with a Jackson Distribution Function (in Longitudinal Velocities).- 2.5. Axial—Symmetrical Perturbations of Cylindrical Models of a More General Type.- § 3. Nonaxial Perturbations of a Collisionless Cylinder.- 3.1. The Long—Wave Fire-Hose Instability.- 3.2. Nonaxial Perturbations of a Cylinder with Circular Particle Orbits 100§ 4. Stability of a Cylinder with Respect to Flute—like Perturbations.- § 5. Local Analysis of the Stability of Cylinders (Flute—like Perturbations).- 5.1. Dispersion Equation for Model (2), § 1.- 5.2. Maxwellian Distribution Function.- § 6. Comparison with Oscillations of an Incompressible Cylinder.- 6.1. Flute—like Perturbations (kz = 0).- § 7. Flute—like Oscillations of a Nonuniform Cylinder with Circular Orbits of Particles.- Problems.- III Equilibrium and Stability of Collisionless Spherically Symmetrical Systems.- § 1. Equilibrium Distribution Functions.- § 2. Stability of Systems with an Isotropic Particle Velocity Distribution.- 2.1. The General Variational Principle for Gravitating Systems with the Isotropic Distribution of Particles in Velocities (f0 = f0(E), f’0 = df0|dE ? 0).- 2.2. Sufficient Condition of Stability.- 2.3. Other Theorems about Stability. Stability with Respect to Nonradial Perturbations.- 2.4. Variational Principle for Radial Perturbations.- 2.5. Hydrodynamical Analogy.- 2.6. On the Stability of Systems with Distribution Functions That Do Not Satisfy the Condition f’0 (E) ? 0.- § 3. Stability of Systems of Gravitating Particles Moving On Circular Trajectories.- 3.1. Stability of a Uniform Sphere.- 3.2. Stability of a Homogeneous System of Particles with Nearly Circular Orbits.- 3.3. Stability of a Homogeneous Sphere with Finite Angular Momentum.- 3.4. Stability of Inhomogeneous Systems.- § 4. Stability of Systems of Gravitating Particles Moving in Elliptical Orbits.- 4.1. Stability of a Sphere with Arbitrary Elliptical Particle Orbits.- 4.2. Instability of a Rotating Freeman Sphere.- § 5. Stability of Systems with Radial Trajectories of Particles.- 5.1. Linear Stability Theory.- 5.2. Simulation of a Nonlinear Stage of Evolution.- § 6. Stability of Spherically Symmetrical Systems of General Form.- 6.1. Series of the Idlis Distribution Functions.- 6.2. First Series of Camm Distribution Functions (Generalized Poly tropes).- 6.3. Shuster’s Model in the Phase Description.- §7. Discussion of the Results.- Problems.- IV Equilibrium and Stability of Collisionless Ellipsoidal Systems.- § 1. Equilibrium Distribution Functions.- 1.1 Freeman’s Ellipsoidal Models.- 1.2. “Hot” Models of Collisionless Ellipsoids of Revolution.- § 2. Stability of a Three—Axial Ellipsoid and an Elliptical Disk.- 2.1. Stability of a Three-Axial Ellipsoid.- 2.2. Stability of Freeman Elliptical Disks.- § 3. Stability of Two—Axial Collisionless Ellipsoidal Systems.- 3.1. Stability of Freeman’s Spheroids.- 3.2. Peebles—Ostriker Stability Criterion. Stability of Uniform Ellipsoids, “Hot” in the Plane of Rotation.- 3.3. The Fire-Hose Instability of Ellipsoidal Stellar Systems.- 3.4. Secular and Dynamical Instability. Characteristic Equation for Eigenfrequencies of Oscillations of Maclaurin Ellipsoids.- Problems.- V Equilibrium and Stability of Flat Gravitating Systems.- § 1. Equilibrium States of Flat Gaseous and Collisionless Systems.- 1.3. Systems with Circular Particle Orbits.- 1.4. Plasma Systems with a Magnetic Field.- 1.5. Gaseous Systems.- 1.6. “Hot” Collisionless Systems.- § 2. Stability of a “Cold” Rotating Disk.- 2.1. Membrane Oscillations of the Disk.- 2.2. Oscillations in the Plane of the Disk.- § 3. Stability of a Plasma Disk with a Magnetic Field.- 3.1. Qualitative Derivation of the Stability Condition.- 3.2. Variational Principle.- 3.3. Short—Wave Approximation.- 3.4. Numerical Analysis of a Specific Model.- § 4. Stability of a “Hot” Rotating Disk.- 4.1. Oscillations in the Plane of the Disk.- 4.2. Bending Perturbations.- 4.3. Methods of the Stability Investigation of General Collisionless Disk Systems.- 4.4. Exact Spectra of Small Perturbations.- 4.5. Global Instabilities of Gaseous Disks. Comparison of Stability Properties of Gaseous and Stellar Disks.- Problems.- References.- Additional References.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Physics of Gravitating Systems II: Nonlinear Collective Processes: Nonlinear Waves, Solitons, Collisionless Shocks, Turbulence. Astrophysical Applications
Table of Contents(Volume II).- Non-Jeans Instabilities of Gravitating Systems.- VI Non-Jeans Instabilities of Gravitating Systems.- § 1. Beam Instability of a Gravitating Medium.- 1.1. Theorem of a Number of Instabilities of the Heterogeneous System with Homogeneous Flows.- 1.2. Expression for the Growth Rate of the Kinetic Beam Instability in the Case of a Beam of Small Density (for an Arbitrary Distribution Function).- 1.3. Beam with a Step Function Distribution.- 1.4. Hydrodynamical Beam Instability. Excitation of the Rotational Branch.- 1.5. Stabilizing Effect of the Interaction of Gravitating Cylinders and Disks.- 1.6. Instability of Rotating Inhomogeneous Cylinders with Oppositely Directed Beams of Equal Density.- § 2. Gradient Instabilities of a Gravitating Medium.- 2.1. Cylinder of Constant Density with Radius-Dependent Temperature. Hydrodynamical Instability.- 2.2. Cylinder of Constant Density with a Temperature Jump. Kinetic Instability.- 2.3. Cylinder with Inhomogeneous Density and Temperature.- § 3. Hydrodynamical Instabilities of a Gravitating Medium with a Growth Rate Much Greater than that of Jeans.- 3.1. Hydrodynamical Instabilities in the Model of a Flat Parallel Flow.- 3.2. Hydrodynamical Instabilities of a Gravitating Cylinder.- §4. General Treatment of Kinetic Instabilities.- 4.1. Beam Effects in the Heterogeneous Model of a Galaxy.- 4.2. Influence of a “Black Hole” at the Center of a Spherical System on the Resonance Interactions Between Stars and Waves.- 4.3. Beam Instability in the Models of a Cylinder and a Flat Layer.- VII Problems of Nonlinear Theory.- § 1. Nonlinear Stability Theory of a Rotating, Gravitating Disk.- 1.1. Nonlinear Waves and Solitons in a Hydrodynamical Model of an Infinitely Thin Disk with Plane Pressure.- 1.2. Nonlinear Waves in a Gaseous Disk.- 1.3. Nonlinear Waves and Solitons in a Stellar Disk.- 1.4. Explosive Instability.- 1.5. Remarks on the Decay Processes.- 1.6. Nonlinear Waves in a Viscous Medium.- § 2. Nonlinear Interaction of a Monochromatic Wave with Particles in Gravitating Systems.- 2.1. Nonlinear Dynamics of the Beam Instability in a Cylindrical Model.- 2.2. Nonlinear Saturation of the Instability at the Corotation Radiusin the Disk.- § 3. Nonlinear Theory of Gravitational Instability of a Uniform Expanding Medium.- § 4. Foundations of Turbulence Theory.- 4.1. Hamiltonian Formalism for the Hydrodynamical Model of a Gravitating Medium.- 4.2. Three-Wave Interaction.- 4.3. Four-Wave Interaction.- §5. Concluding Remarks.- 5.1. When Can an Unstable Gravitating Disk be Regarded as an Infinitesimally Thin One?.- 5.2. On Future Soliton Theory of Spiral Structure.- Problems.- II Astrophysical Applications.- VIII General Remarks.- § 1. Oort’s Antievolutionary Hypothesis.- § 2. Is There a Relationship Between the Rotational Momentum of an Elliptical Galaxy and the Degree of Oblateness?.- § 3. General Principles of the Construction of Models of Spherically Symmetric Systems.- § 4. Lynden-Bell’s Collisionless Relaxation.- § 5. Estimates of “Collisionlessness” of Particles in Different Real Systems.- IX Spherical Systems.- § 1. A Brief Description of Observational Data.- 1.1. Globular Star Clusters.- 1.2. Spherical Galaxies.- 1.3. Compact Galactic Clusters.- § 2. Classification of Unstable Modes in Scales.- § 3. Universal Criterion of the Instability.- § 4. Specificity of the Effects of Small-Scale and Large-Scale Perturbations on the System’s Evolution.- § 5. Results of Numerical Experiments for Systems with Parameters Providing Strong Supercriticality.- § 6. Example of Strongly Unstable Model.- § 7. Can Lynden-Bell’s Intermixing Mechanism Be Observed Against a Background of Strong Instability ?.- § 8. Is the “Unstable” Distribution of Stellar Density Really Unstable (in the Hydrodynamical Sense) in the Neighborhood of a “Black Hole”?.- X Ellipsoidal Systems.- § 1. Objects Under Study.- § 2. Elliptical Galaxies.- 2.1. Why Are Elliptical Galaxies More Oblate than E7 Absent?.- 2.2. Comparison of the Observed Oblatenesses of S- and SO-Galaxies with the Oblateness of E-Galaxies.- 2.3. Two Possible Solutions of the Problem.- 2.4. The Boundary of the Anisotropic (Fire-Hose) Instability Determines the Critical Value of Oblateness.- 2.5. Universal Criterion of Instability.- §3. SB-Galaxies.- 3.1. The Main Problem.- 3.2. Detection in NGC 4027 of Counterflows as Predicted by Freeman.- 3.3. Stability of Freeman Models of SB-Galaxies with Observed Oblateness.- XI Disk-like Systems. Spiral Structure.- § 1. Different Points of View on the Nature of Spiral Structure.- § 2. Resonant Interaction of the Spiral Wave with Stars of the Galaxy.- 2.1. Derivation of Expressions for the Angular Momentum and Energy of the Spiral Wave.- 2.2. Physical Mechanisms of Energy and Angular Momentum Exchange Between the Spiral Waves and the Resonant Stars.- § 3. The Linear Theory of Stationary Density Waves.- 3.1. The Primary Idea of Lin and Shu of the Stationary Density Waves.- 3.2. The Spiral Galaxy as an Infinite System of Harmonic Oscillators.- 3.3. On “Two-Armness” of the Spiral Structure.- 3.4. The Main Difficulties of the Stationary Wave Theory of Lin and Shu.- §4. Linear Theory of Growing Density Waves.- 4.1. Spiral Structure as the Most Unstable Mode.- 4.2. Gravitational Instability at the Periphery of Galaxies.- 4.3. Waves of Negative Energy Generated Near the Corotation Circle and Absorbed at the Inner Lindblad Resonance—Lynden-BellKalnaj’s Picture of Spiral Pattern Maintenance.- 4.4. Kelvin–Helmholz Instability and Flute-like Instability in the Near-Nucleus Region of the Galaxy as Possible Generators of Spiral Structure.- 4.5. The “Trailing” Character of Spiral Arms.- § 5. Comparison of the Lin–Shu Theory with Observations.- 5. 1 The Galaxy.- 5.2. M33, M51, M81.- § 6. Experimental Simulation of Spiral Structure Generation.- 6. 1 In a Rotating Laboratory Plasma.- 6.2. In Numerical Experiment.- § 7. The Hypothesis of the Origin of Spirals in the SB-Galaxies.- XII Other Applications.- § 1 On the Structure of Saturn’s Rings.- l.1. Introduction.- 1.2. Model. Basic Equations.- 1.3. Jeans Instability.- 1.4. Dissipative Instabilities.- 1.5. Modulational Instability.- Appendix. Derivation of the Expression for the Perturbation Energy of Maclaurin’s Ellipsoid.- § 2. On the Law of Planetary Distances.- §3. Galactic Plane Bending.- 3.1. Quasistationary Tidal Deformation.- 3.2. Free Modes of Oscillations.- 3.3. Close Passage.- § 4. Instabilities in Collisions of Elementary Particles.- § 1. Collisionless Kinetic Equation and Poisson Equation in Different Coordinate Systems.- § 2. Separation of Angular Variables in the Problem of Small Perturbations of Spherically Symmetrical Collisionless Systems.- § 3. Statistical Simulation of Stellar Systems.- 3.1. Simulation of Stellar Spheres of the First Camm Series.- 3.2. Simulation of Homogeneous Nonrotating Ellipsoids.- § 4. The Matrix Formulation of the Problem of Eigenoscillations of a Spherically-Symmetrical Collisionless System.- § 5. The Matrix Formulation of the Problem of Eigenoscillations of Collisionless Disk Systems.- 5.1. The Main Ideas of the Derivation of the Matrix Equation.- 5.2. “Lagrange” Derivation of the Matrix Equation.- § 6. Derivation of the Dispersion Equation for Perturbations of the Three-Axial Freeman Ellipsoid.- § 7. WKB Solutions of the Poisson Equation Taking into Account the Preexponential Terms and Solution of the Kinetic Equation in the Postepicyclic Approximation.- 7.1. The Relation Between the Potential and the Surface Density.- 7.2. Calculations of the Response of a Stellar Disk to an Imposed Perturbation of the Potential.- § 8. On the Derivation of the Nonlinear Dispersion Equation for Collisionless Disk.- § 9. Calculation of the Matrix Elements for the Three-Waves Interaction.- § 10. Derivation of the Formulas for the Boundaries of Wave Numbers Range Which May Take Part in a Decay.- §11. Derivation of the Kinetic Equation for Waves.- § 12. Table of Non-Jeans Instabilities (with a Short Summary).- References.- Additional References.
£42.74
Springer Fachmedien Wiesbaden Die Spezielle Relativitätstheorie: Einsteins Welt
Book SynopsisDie Spezielle Relativitätstheorie steht und fällt mit der universellen Konstanz der Lichtgeschwindigkeit. Darauf gründet die Einstein-Minkowski-Axiomatik, die wegen ihrer grundsätzlichen Bedeutung in keinem Lehrbuch zur Theoretischen Physik fehlen darf. Hier soll außerdem auf eine zweite, unabhängige, aber vollkommen äquivalente axiomatische Darstellung aufmerksam gemacht werden, die weniger abstrakt und daher geeignet ist, auch demjenigen einen Einstieg in die relativistische Welt zu erschließen, der nicht unbedingt theoretischer Physiker werden will. Dabei geht es dann primär um den Gang von bewegten und ruhenden Uhren und die Längen von bewegten und ruhenden Maßstäben. Ganz wesentlich ist es, von Anfang an den definitorischen Charakter bei der Bestimmung des Begriffes der Gleichzeitigkeit zu verstehen. Der sorgfältige Umgang mit dieser Definition liefert den Schlüssel zur Auflösung der relativistischen Paradoxa, wie dies ausführlich beim Zwillingsparadoxon gezeigt wird. Die Unterscheidung von Korrelation und Wechselwirkung erlaubt eine Betrachtung von Tachyonen, ohne die Kausalität zu verletzen. Anhand eines Gittermodells der relativistischen Raum-Zeit kann am Ende sogar das Zustandekommen der Längenkontraktion, der Zeitdilatation und der relativistischen Massenformel veranschaulicht werden. Es werden die Schlüsselexperimente erklärt und 48 Übungsaufgaben vorgerechnet.Table of ContentsDas Relativitätsprinzip: klassische und relativistische Raum-Zeit.- Energie - Masse - Äquivalenz.- Relativistische Phänomene und Paradoxa.- Die Darstellungen der Lorentz-Gruppe.- Mechanik, Elektrodynamik, Weyl-Gleichung, Dirac-Gleichung, Pauli-Gleichung.- Ein Gittermodell der relativistischen Raum-Zeit.
£85.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Astrophysics of Black Holes: From Fundamental Aspects to Latest Developments
Book SynopsisThis book discusses the state of the art of the basic theoretical and observational topics related to black hole astrophysics. It covers all the main topics in this wide field, from the theory of accretion disks and formation mechanisms of jet and outflows, to their observed electromagnetic spectrum, and attempts to measure the spin of these objects. Black holes are one of the most fascinating predictions of general relativity and are currently a very hot topic in both physics and astrophysics. In the last five years there have been significant advances in our understanding of these systems, and in the next five years it should become possible to use them to test fundamental physics, in particular to predict the general relativity in the strong field regime. The book is both a reference work for researchers and a textbook for graduate students. Trade Review“A perfect volume for young scientists starting their research in a field of astrophysics of black holes. The book presents very deep and broad knowledge on the topic, in a well-written form, which can easily be understood by the reader. It is also very good position for more advanced scientists as well.” (Hubert Siejkowski, Pure and Applied Geophysics, Vol 175, 2018)Table of ContentsPreface.- Black Hole Accretion Discs.- Black hole X-ray binaries.- Measuring spin: implications for our understanding of black hole accretion physics.- Jet and wind from black hole accretion flows.- Gravitational Waves: a new tool for observing the Universe.- A brief review of relativistic gravitational collapse.- General relativity in a nutshell.
£71.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Supergravity: From First Principles to Modern Applications
Book SynopsisThis book is about supergravity, which combines the principles of general relativity and local gauge invariance with the idea of supersymmetries between bosonic and fermionic degrees of freedom. The authors give a thorough and pedagogical introduction to the subject suitable for beginning graduate or advanced undergraduate students in theoretical high energy physics or mathematical physics. Interested researchers working in these or related areas are also addressed. The level of the presentation assumes a working knowledge of general relativity and basic notions of differential geometry as well as some familiarity with global supersymmetry in relativistic field theories. Bypassing curved superspace and other more technical approaches, the book starts from the simple idea of supersymmetry as a local gauge symmetry and derives the mathematical and physical properties of supergravity in a direct and “minimalistic” way, using a combination of explicit computations and geometrical reasoning. Key topics include spinors in curved spacetime, pure supergravity with and without a cosmological constant, matter couplings in global and local supersymmetry, phenomenological and cosmological implications, extended supergravity, gauged supergravity and supergravity in higher spacetime dimensions.Table of ContentsIntroduction.- From Global to Local SUSY.- Gravity and spinors.- D=4 N=1 SUGRA.- Matter couplings in global SUSY.- Matter couplings in SUGRA.- SUGRA phenomenology.- Extended supergravities.- Gauged supergravity.- SUGRA in any dimension.
£52.24
Springer The Small the Big and the Ugly
Book Synopsis
£26.59
Springer Fachmedien Wiesbaden Einsteins Relativitätstheorie und die Geometrien
Book SynopsisDer Faszination zweier scheinbar getrennter Gebiete - der Relativitätstheorie und der Geometrie - folgt dieses Buch: Thema ist die Geometrie in Raum und Zeit. Die Bewegung in Raum und Zeit bestimmt geometrische Konstruktionen, die jenseits der euklidischen Geometrie immer noch deren Klarheit und Zusammenhang bewahren. Dabei ist die Verblüffung zweiseitig: Relativitätstheorie wird Geometrie und Geometrie findet physikalische Entsprechung. Auf der einen Seite offenbaren sich in richtig konstruierten Abbildungen ohne komplizierte Formeln die erstaunlichen Ergebnisse der Relativitätstheorie und ihre Widerspruchsfreiheit. Auf der anderen Seite ergeben sich ganz ungewohnte und unerwartete, aber physikalisch bedeutsame einfache Beispiele für nichteuklidische Geometrien, in denen noch mit Gerade und Kegelschnitt konstruiert werden kann.Trade Review"Mit diesem Buch ist dem Autor nicht nur ein wichtiger Beitrag zur Revitalisierung teilweise in Vergessenheit geratener Zusammenhänge gelungen. Auch die Didaktik der Relativitätstheorie und Geometrie sowie deren Wechselbeziehung profitiert davon." Praxis der Naturwissenschaften, 03/2003Table of Contents1 Einleitung.- 2 Die Welt aus Raum und Zeit.- 2.1 Fahrpläne.- 2.2 Die Vermessung von Raum und Zeit.- 3 Spiegelung und Stoß.- 3.1 Geometrie und Spiegelung.- 3.2 Die Spiegelung mechanischer Bewegung.- 4 Relativitätsprinzip der Mechanik und Wellenausbreitung.- 5 Die Relativitätstheorie und ihre Paradoxa.- 5.1 Pseudoeuklidische Geometrie.- 5.2 Einsteinsche Mechanik.- 5.3 Kinematische Besonderheiten.- 5.4 Das Netz.- 5.5 Schneller als das Licht.- 6 Die Hyperbel als Kreis.- 7 Krümmung.- 7.1 Kugel und Massenschale.- 7.2 Der Kosmos.- 8 Die projektive Wurzel.- 9 Die neun Geometrien der Ebene.- 10 Allgemeines.- 10.1 Relativitätstheorie.- 10.2 Geometrie und Physik.- A Spiegelungen.- B Transformationen.- B.1 Koordinaten.- B.2 Inertialsysteme.- B.3 Riemann-Räume, Einstein-Welten.- C Projektive Geometrie.- C.1 Algebra.- C.2 Projektive Abbildungen.- C.3 Kegelschnitte.- D Der Übergang von der projektiven zur metrischen Ebene.- D.1 Die Polarität.- D.2 Die Spiegelung.- D.3 Der Geschwindigkeitsraum.- D.4 Kreise und Peripherien.- D.5 Zwei Beispiele.- E Die metrische Ebene.- E.1 Klassifikation.- E.2 Die Metrik.- Übungsaufgaben.
£34.19
Springer Fachmedien Wiesbaden Relativitätstheorie
Book SynopsisDieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.Table of ContentsGrundlagen der speziellen Relativitätstheorie.- Mathematische Hilfsmittel.- Weiterer Ausbau der speziellen Relativitätstheorie.- Allgemeine Relativitätstheorie.- Theorien über die Natur der elektrischen Elementarteilchen.
£66.49
Springer Fachmedien Wiesbaden Spezielle Relativitätstheorie: Ein neuer Einstieg
Book SynopsisKann man die Spezielle Relativitätstheorie ebenso begreifen wie das Funktionieren eines Fahrrades oder eines Autos? Die Relativitätstheorie wurde durch Einsteins Geniestreich aus der Taufe gehoben, wodurch ein Gebirge von Problemen überwunden war. Dieses Buch bietet Ihnen einen fundierten und gut verständlichen Einstieg in eines der faszinierendsten Gebiete der Physik.Trade Review"Es kann allen als Lektüre empfohlen werden, die sich für das entsprechende Thema interessieren." ZAMM 88, 2008 "Ein Buch also, von dessen Lektüre jeder ohne Zweifel profitieren wird, der auch nur ansatzweise über den Rand des üblicherweise präsentierten Methodencocktails hinausblicken möchte." ImpulsE, 12/2007Table of ContentsRaum - Zeit - Bewegung - Das Relativitätsprinzip - Elementarer Aufbau der klassischen Raum-Zeit - Elementarer Aufbau der relativistischen Raum-Zeit - Die ganze Theorie auf einer Seite - Die Newtonsche Mechanik - Einsteins Energie-Masse-Äquivalenz - Relativistische Phänomene und Paradoxa - Der mathematische Formalismus der Speziellen Relativitätstheorie
£26.59
World Scientific Publishing Co Pte Ltd Breakdown Of Einstein's Equivalence Principle
Book SynopsisAn equality between inertial and gravitational masses was established by Galileo Galilei more than 400 years ago and was accepted by Albert Einstein as a key point of his theory of gravitation — General Relativity. The above mentioned equality is called the Equivalence Principle. In this pioneering book, some unusual situations are described, where the Equivalence Principle is theoretically broken, and the possible experiments, where such breakdowns can be observed, are discussed in a brief. It is known that, in standard situations, the Equivalence Principle is extremely well established on Earth and in space in numerous experiments, including experiments during the recent space mission MICROSCOPE. Therefore, this book suggests a real breakthrough in the better understanding of Einstein's gravitational theory and its relation to quantum mechanics, which is a definite step towards the so-called 'Theory of Everything'. This book is recommended for all readers who are interested in gravitation and General Relativity.
£58.50
Springer Verlag, Singapore Black Holes: A Laboratory for Testing Strong Gravity
Book Synopsis This textbook introduces the current astrophysical observations of black holes, and discusses the leading techniques to study the strong gravity region around these objects with electromagnetic radiation. More importantly, it provides the basic tools for writing an astrophysical code and testing the Kerr paradigm. Astrophysical black holes are an ideal laboratory for testing strong gravity. According to general relativity, the spacetime geometry around these objects should be well described by the Kerr solution. The electromagnetic radiation emitted by the gas in the inner part of the accretion disk can probe the metric of the strong gravity region and test the Kerr black hole hypothesis. With exercises and examples in each chapter, as well as calculations and analytical details in the appendix, the book is especially useful to the beginners or graduate students who are familiar with general relativity while they do not have any background in astronomy or astrophysics.<Table of ContentsIntroduction.- Black Hole Solutions.- Motion around Black Holes.- Astrophysical Black Holes.- Thin Accretion Disks.- Thermal Spectrum of Thin Disks.- Relativistic Iron Line.- Quasi-Periodic Oscillations.- Parametrization of the Background Metric.- Observational Constraints.
£49.49
World Scientific Publishing Co Pte Ltd Pull Of History, The: Human Understanding Of
Book SynopsisThis book seeks to understand what bring to pass the birth of modern physics by focusing upon the formation of the concept of force. This would be the first book to note the important role magnetism has played in this process. Indeed, the force between celestial bodies, before the introduction of the Isaac Newtonian gravitational force, is first introduced by Johannes Kepler by analogy with the magnetic force. Moreover, this book, by concentrating our attention on the magnetism, fully describes the developments and the recognition of the force concept during the Middle Ages. The detailed description of the Middle Ages and the Renaissance is a strong point of this book. By discussing and emphasizing on the role accomplished by the magnetic force, this book makes clear the connection between the natural magic and the modern experimental physics. This book will open up a new aspect of the birth of modern physics.
£156.60
Teacher Created Materials, Inc Gravitational Interactions
£10.44
Independently Published A Quantum Theory of Color Strings: A Palette of Gluons
£11.05
Nova Science Publishers Inc Scalar Strong Interaction Hadron Theory III
Book Synopsis
£163.19
