Geometrical Methods of Mathematical Physics

by Bernard F. Schutz

In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.

Genres: Physics, Mathematics, Textbooks, Science, Technical, Reference

264 pages, Paperback

First published January 1, 1980

Reviews

[Israeliano · Rating 3 out of 5]

A book about geometry, without pullback, pushforward, is not an excellent book. Furthermore, it explanation of Lie derivative is clear only in hindsight. Finally, its explanation about gauge symmetry as a connection deserve more space, way more space. Overall, the book is a nice first read, not trying to go too deep, specially when clarifying the curl (amazingly, some physicist still don't know this!) But it lacks several concepts and a more precise development of some ideas, besides the bad explanation of the Lie derivative.

[Susmit Islam · Rating 5 out of 5]

Differential Geometry is the sort of subject that really embodies what it encodes - DG is sort of like a manifold that is best covered by several different coordinate systems. Different books give you those different coordinate systems to view the subject through. Schutz was a particularly good one for me. Serves as a great middle-ground between the DG in intermediate GR texts and advanced GR/DG texts. Lots of pictures. And keeps reminding you which structures on a manifold are metric-dependent and which are not so you don't confound (differential) topological properties of the manifold with its metrical properties. Good to have beside you to look things up for more intuition when going through your GR book.