Classical Mathematical Physics: Dynamical Systems and Field Theories - Hardcover

by Walter Thirring (Author), E. M. Harrell (Translator)

I Classical Dynamical Systems.- 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.- 3.2 Hamilton's Equations.- 3.3 Constants of Motion.- 3.4 The Limit t ? ?.- 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 Motion.- 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.- II Classical Field Theory.- 7 Introduction to Classical Field Theory.- 7.1 Physical Aspects of Field Dynamics.- 7.2 The Mathematical Formalism.- 7.3 Maxwell's and Einstein's Equations.- 8 The Electromagnetic Field of a Known Charge Distribution.- 8.1 The Stationary-Action Principle and Conservation Theorems.- 8.2 The General Solution.- 8.3 The Field of a Point Charge.- 8.4 Radiative Reaction.- 9 The Field in the Presence of Conductors.- 9.1 The Superconductor.- 9.2 The Half-Space, the Wave-Guide, and the Resonant Cavity.- 9.3 Diffraction at a Wedge.- 9.4 Diffraction at a Cylinder.- 10 Gravitation.- 10.1 Covariant Differentiation and the Curvature of Space.- 10.2 Gauge Theories and Gravitation.- 10.3 Maximally Symmetric Spaces.- 10.4 Spaces with Maximally Symmetric Submanifolds.- 10.5 The Life and Death of Stars.- 10.6 The Existence of Singularities.

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This volume combines the enlarged and corrected editions of both volumes on classical physics of Thirring's famous course in mathematical physics. With numerous examples and remarks accompanying the text, it is suitable as a textbook for students in physics, mathematics, and applied mathematics.