Classical Mathematical Physics: Dynamical Systems and Field Theories

✍ Scribed by Walter Thirring

• Publisher: Springer
• Year: 1997
• Tongue: English
• Leaves: 573
• Edition: 3
• Category: Library

✦ Synopsis

Trans. by E. M. Harrell

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

Front Matter....Pages i-xxviii
Front Matter....Pages 1-1
Introduction....Pages 3-9
Analysis on Manifolds....Pages 11-87
Hamiltonian Systems....Pages 89-168
Nonrelativistic Motion....Pages 169-212
Relativistic Motion....Pages 213-263
The Structure of Space and Time....Pages 265-281
Front Matter....Pages 283-283
Introduction to Classical Field Theory....Pages 285-328
The Electromagnetic Field of a Known Charge Distribution....Pages 329-381
The Field in the Presence of Conductors....Pages 383-432
Gravitation....Pages 433-528
Back Matter....Pages 529-543

✦ Subjects

Theoretical, Mathematical and Computational Physics