The Geometry of Physics: An Introduction

by Theodore Frankel

This book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism, thermodynamics, the deformation tensors of elasticity, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should also be of interest to mathematics students. This book will be useful to graduate and advanced undergraduate students of physics, engineering and mathematics. It can be used as a course text or for self study.

Genres: Physics, Mathematics, Science, Geometry, Textbooks, Reference, Nonfiction

678 pages, Paperback

First published January 28, 1997

Reviews

[Robert · Rating 5 out of 5]

This is my favorite book on mathematical physics. We used the pre-published edition in graduate school. I bought the first edition as soon as it came out. Super book for anyone who wants to learn about the mathematics used in Physics, from the point of view of a mathematician.

[Ryan · Rating 5 out of 5]

The overview chapter to the third edition is invaluable.

[Toby Bartels · Rating 5 out of 5]

If you wish to apply geometry to physics, then you must read this book. There is no alternative. This is the material that matters —any other approach is deficient. There is no better exposition than in this text. Yes, it is hard going; there is a lot to learn, and there is even more to unlearn. But you must read it.

[Dave]

I really like the exposition in this book.

[Joe Cole · Rating 5 out of 5]

Frankel did a great job with this book. A mathematician can enjoy this book even though it is mathematical physics. The mathematics is presented in very nice form.

[Zudar Zulfiqar]

goood as hell , thank you