Classical Mathematical Physics: Dynamical Systems and Field Theories [Hardcover]

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

Book Description

Publication Date: October 10, 1997 | ISBN-10: 0387948430 | ISBN-13: 978-0387948430 | Edition: 3rd ed.

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.

Editorial Reviews

Review

From the reviews:

"… A complete book in classical field theory. Moreover it is very interesting to see the geometry of relativity. I highly recommend this book for the theoretical physicists and mathematicians interested in physics. In short this is a very useful book."  H. Cebeci, Middle East Technical University, Ankara, Turkey

Product Details

• Hardcover: 543 pages
• Publisher: Springer; 3rd ed. edition (October 10, 1997)
• Language: English
• ISBN-10: 0387948430
• ISBN-13: 978-0387948430
• Product Dimensions: 9.4 x 6.2 x 1.2 inches
• Shipping Weight: 2.3 pounds
• Average Customer Review: 4.0 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #1,772,797 in Books (See Top 100 in Books)

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23 of 24 people found the following review helpful:

5.0 out of 5 stars Classical physics wrote anew by a master, July 26, 1998

By 

henrique fleming - See all my reviews

This review is from: Classical Mathematical Physics: Dynamical Systems and Field Theories (Hardcover)

Walther Thirring is a very well known quantum field theorist. He made important contributions to applications of dispersion relations to particle physics, wrote a book on quantum electrodynamics that was so good that Dyson compared it to Pauli's famous quantum mechanics article in the Handbuch der Physik, invented the famous Thirring model, a two-dimensional quantum field with exact (that is, non perturbative) solutions, and produced, with Elliot Lieb, the best demonstration of the stability of matter.At a point in his career he decided to show his fellows what they were losing by ignoring the modern mathematics. Having lectured in mathematical physics, he published his lecture notes, and, later, transformed them into a book of 4 volumes. The present book is a translation, improvement and fusion of the two first volumes, covering Dynamical Systems, that is advanced mechanics and field theories, meaning electrodynamics, gravitation and a little of classical gauge field t! heory. Having done work qualified as high-class mathematics, he is one of the very few scientists of our day who excelled both in physics and mathematics. The book reflects this virtue. I would venture to say that his personal basic reference was the monumental "Traite d'analyse" by Jean Dieudonne'. Not only is this the first of his references, but the way of introducing differential manifolds, and, particularly, tangent spaces, is very close to Dieudonne's. Once you learn what Thirring is offering you, you will adopt the new methods. They are much more natural, which, in mathematics, is tantamount to being deeper. And the methods are also much more efficient for calculations. Take this problem: given a (semi-)riemannian metric, compute the components of the curvature tensor (a problem central to general relativity). You can do it by using classical tensors, as most textbooks do (take Weinberg, for instance), or use Cartan structural equations, which use exterior di! fferential forms (as in Thirring). I benchmarked it: for th! e usual metrics, you gain, in speed, a factor 5 (by following Thirring). Still more important, being much shorter, the calculation is much less prone to errors. In this text I especially liked the sections on the Action Principle and the Noether theorem, in the garb of differential forms, which is, no doubt, their natural language. This is a very compact book. You are supposed to work hard, and it is absolutely essential that you work out the exercises (all of them) and check the solutions. But, of course, this advice applies to every book!

14 of 15 people found the following review helpful:

5.0 out of 5 stars The way mathematical physics ought to be taught, December 28, 2001

By 

Assaf Tal (Israel) - See all my reviews

This review is from: Classical Mathematical Physics: Dynamical Systems and Field Theories (Hardcover)

This book represents how a graduate course in mathematical physics ought to look like. It deals with two topics with which the reader should be very familiar, physics-speaking: particle dynamics and classical fields (e.g. Maxwell's equations). Therefore the author is justified in neglecting the physics and concentrating on the mathematics; in fact, introducing the mathematical tools using such old friends makes it easier for the reader to fully understand the mathematics, and the way it relates to the physics.
There are many books on the market that teach differential geometry - Frankel's "geometry and physics", Bishop and Goldberg's "Tensor analysis on manifolds" and countless others - but this book is something more: it deals as much with mathematical physics as it deals with the mathematics. For instance, it formulates hamiltonian mechanics for a particle in an electromagnetic field and proceeds to solve the cases of the constant field, coloumb field, travelling plane disturbances and more, all using the modern language of differential geometry all physicists should know.
Although the book contains an introduction to differential geometry - which is very nice, actually, with plenty of examples and such - I strongly advise the reader to use another book as a main source book for diff. geometry, and to use Thirring's book as a supplement. Thirring's strength is not in teaching diff. geometry, it is in showing how to apply it to physics.
It almost goes without saying, p.s., that the reader should have a good grasp of calculus in R^n, topology and linear algebra before approaching this book.

3 of 3 people found the following review helpful:

5.0 out of 5 stars Very good and useful book, October 28, 1999

By 

HAKAN CEBECI (Ankara,Turkey) - See all my reviews

This review is from: Classical Mathematical Physics: Dynamical Systems and Field Theories (Hardcover)

This book introduces the physicists applications of differential geometry in physics.It is a complete book in classical field theory.Moreover it is very interesting to see the geometry of relativity.I highly recommend this book for the theoretical physicists and the mathematicians interested in physics.In short this is a very useful book.