The Geometry of Physics: An Introduction [Paperback]

Theodore Frankel (Author)

Book Description

ISBN-10: 0521387531 | ISBN-13: 978-0521387538 | Publication Date: April 13, 1999 | Edition: Revised

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.

Editorial Reviews

Review

' ... extremely helpful for students in physics and engineering ... recommended to a wide audience ...' European Mathematical Society

'The layout, the typography and the illustrations of this advanced textbook on modern mathematical methods are all very impressive and so are the topics covered in the text.' Zentralblatt für Mathematik und ihre Grenzgebiete

Book Description

This book is intended to provide a working knowledge of those parts of geometry that are essential for a deeper understanding of both classical and modern physics and engineering. This book will be useful to graduate and advanced undergraduate students of physics, engineering and mathematics.

Product Details

• Paperback: 678 pages
• Publisher: Cambridge University Press; Revised edition (April 13, 1999)
• Language: English
• ISBN-10: 0521387531
• ISBN-13: 978-0521387538
• Product Dimensions: 10 x 7.1 x 1.3 inches
• Shipping Weight: 2.5 pounds
• Average Customer Review: 4.2 out of 5 stars  See all reviews (19 customer reviews)
• Amazon Best Sellers Rank: #1,071,194 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

90 of 100 people found the following review helpful:

5.0 out of 5 stars THE modern Differential Geometry book for Physicists, February 21, 2000

By 

A graduate student of Physics (Santa Barbara, CA) - See all my reviews

This review is from: The Geometry of Physics: An Introduction (Paperback)

This book introduces the methods of modern differential geometry and its uses in theoretical physics. The only prerequisites are a good working knowledge of multivariable calculus and linear algebra. The book is very much written for a physics audience(i.e. the book is actually READABLE unlike so many graduate texts in mathematics, and there is an emphasis in actually learning how to CALCULATE things, rather than just staring weary eyed at mathematicians beloved polished proofs that only they can understand) There is an emphasis on physical understanding of the mathematical structures and not too many proofs. Proving things is not a bad thing, but Dr. Frankel seems to know when its most appropriate to do this, and doesn't get too bogged down in the proofs. There is a lot of material in this book (22 chapters) The book is broken into 3 main sections. The first section is on "Manifolds, Tensors, Exterior Forms" Differential forms are not that familiar to physicsts and this is a great place to learn about them. There is very nice section on how to relate Forms to vector Analysis in 3 space that physicists love dearly (see page 94). The second section is on "Geometry and Topology"-mainly Riemannian Geometry and Some Algebraic Topology like DeRham Cohomology, and the third is "Lie Groups, bundles, and Chern Forms". In this third section there is a Chapter on the Dirac equation, and its relation to Spin geometry. The only thing that the book is lacking is that there is no complex algebraic geometry (for aspiring string theorists). It would be nice if some day Dr. Frankel could write a book on this subject, since at this time none exist. I think that even mathematicians could learn a thing or two from this book. Most of differential geometry originated in Physics, not the reverse.

32 of 34 people found the following review helpful:

4.0 out of 5 stars Not Good For Self Study., January 8, 2001

By A Customer

This review is from: The Geometry of Physics: An Introduction (Paperback)

I picked this book for self-study in order to understand differential topology in physics. It is an excellent book for the breath of ideas applicable to many areas of physics and the author has examples from stat mech, thermo, e & m, classical dynamics as well as relativity. I agree with the previous review that it lacks a sense of direction. Occasionally, Frankel uses a concept without explanation only to define it a hundred pages or so later (e.g. the star operator on em fields). For me these problems made the text tough going. I was frequently derailed by complicated notation (without glossary), lack of direction, and deus ex machina concepts dropped without adequate explanation. Some of the confusion derives from use of coordinates which Frankel finds necessary in order to motivate development of coordinate free forms. It seems that the author could have avoided this as did Darling or introduced Clifford algebra early on. I do not recommend this book for independent study without other texts like Flanders, Darling, Misner Thorne Wheeler, etc. to refer. It would be best to have a tutor guide one through it or re-read it after getting sufficient grounding with other texts. This being said it is valuable addition to my library and I still think highly of Frankel's effort.

22 of 23 people found the following review helpful:

5.0 out of 5 stars You should buy this, despite its flaws, March 3, 2006

By 

E. M. Stoudenmire "Physics student" (Santa Barbara, CA) - See all my reviews
(REAL NAME)   

This review is from: The Geometry of Physics: An Introduction (Paperback)

The other reviews on this page give this book anywhere from 1 to 5 stars, and they are all correct in their own way. The book is inspired, deep and full of physics applications and insights. On the other hand, it skims over mathematical rigor to a large degree and focuses more on defining things, getting a feel for them and moving on to application.

My advice: buy the book for its strengths, and read other books in parallel if you need more rigor. But still, buy it.

Also, things can be confusing on the first two or three reads, but keep at it and you will be glad you did.