Classical Mathematical Physics

by Thirring, Walter; Harrell, Evans M., II

• ISBN13: 9780387406152
• ISBN10: 0387406158
• Edition: 3rd
• Format: Paperback
• Copyright: 2003-10-01
• Publisher: Springer Nature

Summary

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. The treatment of classical dynamical systems uses analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems, canonical transformations, constants of motion, and pertubation theory. Problems discussed in considerable detail include: nonrelativistic motion of particles and systems, relativistic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields uses the language of differenial geometry throughout, treating both Maxwell's and Einstein's equations in a compact and clear fashion. The book includes discussions of the electromagnetic field due to known charge distributions and in the presence of conductors as well as a new section on gauge theories. It discusses the solutions of the Einstein equations for maximally symmetric spaces and spaces with maximally symmetric submanifolds; it concludes by applying these results to the life and death of stars.

Table of Contents

Preface to the Third Edition	v
Preface to the Second Edition: Classical Dynamical Systems	vii
Preface to the Second Edition: Classical Field Theory	ix
Preface to the First Edition	xi
Note About the Translation	xiii
Glossary	xix
Symbols Defined in the Text	xxv
Part I Classical Dynamical Systems
Introduction	3	(8)
Equations of Motion	3	(3)
The Mathematical Language	6	(1)
The Physical Interpretation	7	(4)
Analysis on Manifolds	11	(78)
Manifolds	11	(12)
Tangent Spaces	23	(13)
Flows	36	(9)
Tensors	45	(20)
Differentiation	65	(12)
Integrals	77	(12)
Hamiltonian Systems	89	(80)
Canonical Transformations	89	(7)
Hamilton's Equations	96	(9)
Constants of Motion	105	(17)
The Limit t → ±∞	122	(23)
Perturbation Theory: Preliminaries	145	(12)
Perturbation Theory: The Iteration	157	(12)
Nonrelativistic Motion	169	(44)
Free Particles	169	(4)
The Two-Body Problem	173	(9)
The Problem of Two Centers of Force	182	(8)
The Restricted Three-Body Problem	190	(14)
The N-Body Problem	204	(9)
Relativistic Motion	213	(52)
The Hamiltonian Formulation of the Electrodynamic Equations of Motion	213	(6)
The Constant Field	219	(7)
The Coulomb Field	226	(6)
The Betatron	232	(5)
The Traveling Plane Disturbance	237	(5)
Relativistic Motion in a Gravitational Field	242	(6)
Motion in the Schwarzschild Field	248	(9)
Motion in a Gravitational Plane Wave	257	(8)
The Structure of Space and Time	265	(20)
The Homogeneous Universe	265	(2)
The Isotropic Universe	267	(2)
Me According to Galileo	269	(2)
Me as Minkowski Space	271	(6)
Me as a Pseudo-Riemannian Space	277	(8)
Part II Classical Field Theory
Introduction to Classical Field Theory	285	(44)
Physical Aspects of Field Dynamics	285	(9)
The Mathematical Formalism	294	(18)
Maxwell's and Einstein's Equations	312	(17)
The Electromagnetic Field of a Known Charge Distribution	329	(54)
The Stationary-Action Principle and Conservation Theorems	329	(11)
The General Solution	340	(12)
The Field of a Point Charge	352	(18)
Radiative Reaction	370	(13)
The Field in the Presence of Conductors	383	(50)
The Superconductor	383	(10)
The Half-Space, the Wave-Guide, and the Resonant Cavity	393	(12)
Diffraction at a Wedge	405	(12)
Diffraction at a Cylinder	417	(16)
Gravitation	433	(96)
Covariant Differentiation and the Curvature of Space	433	(19)
Gauge Theories and Gravitation	452	(16)
Maximally Symmetric Spaces	468	(13)
Spaces with Maximally Symmetric Submanifolds	481	(18)
The Life and Death of Stars	499	(13)
The Existence of Singularities	512	(17)
Bibliography	529	(10)
Index	539