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＜電子ブック＞
A Course in Mathematical Physics 1 and 2 : Classical Dynamical Systems and Classical Field Theory / by Walter Thirring
(Springer Study Edition)

版	2nd ed. 1992.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	1992
本文言語	英語
大きさ	XX, 261 p : online resource
著者標目	*Thirring, Walter author SpringerLink (Online service)
件　名	LCSH:Mathematical physics FREE:Mathematical Physics FREE:Mathematical Methods in Physics FREE:Theoretical, Mathematical and Computational Physics
一般注記	1 Introduction -- 1.1 Equations of Motion -- 1.2 The Mathematical Language -- 1.3 The Physical Interpretation -- 2 Analysis on Manifolds -- 2.1 Manifolds -- 2.2 Tangent Spaces -- 2.3 Flows -- 2.4 Tensors -- 2.5 Differentiation -- 2.6 Integrals -- 3 Hamiltonian Systems -- 3.1 Canonical Transformations g -- 3.2 Hamilton’s Equations -- 3.3 Constants of Motion -- 3.4 The Limit t ? I ± ? -- 3.5 Perturbation Theory: Preliminaries -- 3.6 Perturbation Theory: The Iteration -- 4 Nonrelativistic Motion -- 4.1 Free Particles -- 4.2 The Two-Body Problem -- 4.3 The Problem of Two Centers of Force -- 4.4 The Restricted Three-Body Problem -- 4.5 The N-body Problem -- 5 Relativistic Motion -- 5.1 The Hamiltonian Formulation of the Electrodynamic Equations of Motions -- 5.2 The Constant Field -- 5.3 The Coulomb Field -- 5.4 The Betatron -- 5.5 The Traveling Plane Disturbance -- 5.6 Relativistic Motion in a Gravitational Field -- 5.7 Motion in the Schwarzschild Field -- 5.8 Motion in a Gravitational Plane Wave -- 6 The Structure of Space and Time -- 6.1 The Homogeneous Universe -- 6.2 The Isotropic Universe -- 6.3 Me according to Galileo -- 6.4 Me as Minkowski Space -- 6.5 Me as a Pseudo-Riemannian Space -- 1. Introduction -- 1.1 Physical Aspects of Field Dynamics -- 1.2 The Mathematical Formalism -- 1.3 Maxwell’s and Einstein’s Equations -- 2. The Electromagnetic Field of a Known Charge Distribution -- 2.1 The Stationary-Action Principle and Conservation Theorems -- 2.2 The General Solution -- 2.3 The Field of a Point Charge -- 2.4 Radiative Reaction -- 3. The Field in the Presence of Conductors -- 3.1 The Superconductor -- 3.2 The Half-Space, the Wave-Guide, and the Resonant Cavity -- 3.3 Diffraction at a Wedge -- 3.4 Diffraction at a Cylinder -- 4. Gravitation -- 4.1 Covariant Differentiation and the Curvature of Space -- 4.2Gauge Theories and Gravitation -- 4.3 Maximally Symmetric Spaces -- 4.4 Spaces with Maximally Symmetric Submanifolds -- 4.5 The Life and Death of Stars -- 4.6 The Existence of Singularities The last decade has seen a considerable renaissance in the realm of classical dynamical systems, and many things that may have appeared mathematically overly sophisticated at the time of the first appearance of this textbook have since become the everyday tools of working physicists. This new edition is intended to take this development into account. I have also tried to make the book more readable and to eradicate errors. Since the first edition already contained plenty of material for a one­ semester course, new material was added only when some of the original could be dropped or simplified. Even so, it was necessary to expand the chap­ ter with the proof of the K-A-M Theorem to make allowances for the cur­ rent trend in physics. This involved not only the use of more refined mathe­ matical tools, but also a reevaluation of the word "fundamental. " What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler's laws, which determine the radii of the planetary orbits, and which used to be passed over in silence as mystical nonsense, seem to point the way to a truth unattainable by superficial observation: The ratios of the radii of Platonic solids to the radii of inscribed Platonic solids are irrational, but satisfy algebraic equations of lower order HTTP:URL=https://doi.org/10.1007/978-1-4684-0517-0

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