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The Geometry of Physics, by Theodore Frankel
Download PDF The Geometry of Physics, by Theodore Frankel
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This book provides 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 (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.
- Sales Rank: #379194 in eBooks
- Published on: 2011-11-03
- Released on: 2013-05-22
- Format: Kindle eBook
Review
"It contains a wealth of interesting material for both the beginning and the advanced levels. The writing may feel informal but it is precise - a masterful exposition. Users of this "introduction" will be well prepared for further study of differential geometry and its use in physics and engineering.
As did earlier editions, this third edition will continue to promote the language with which mathematicians and scientists can communicate."
Jay P. Fillmore, University of California, San Diego for SIAM Review
About the Author
Theodore Frankel received his PhD from the University of California, Berkeley. He is currently Emeritus Professor of Mathematics at the University of California, San Diego.
Most helpful customer reviews
49 of 53 people found the following review helpful.
Third Edition Best of Class & Only Modern Text in this Genre
By Let's Compare Options Preptorial
Some texts are designed to increase understanding, others to aid in practical computation, making them as much references as pedagogic tools. The latter are especially suited for self study. In this new edition, Frankel does something amazing-- instead of completely reorganizing an already stellar text, he "ties it all together" with a new "example" introduction-- a 34 page (roman numeral numbered!) "preface" illustrating Cartan's exterior differential forms with a "metal torsion" example application to Cauchy's stress tensor.
Don't mistakely think that this means Frankel limits this text to the differential geometry of engineering mechanics and materials-- he covers a vast field of physics all the way from classic to quantum, sans string but with numerous gauge applications, in 750 packed pages, most containing fully worked out calculations for the aforementioned reference value.
It seems today that all publishers just parrot "for grad students or advanced undergrads with a year of calculus and some linear algebra." Is this to sell more books? Not sure, but I wouldn't tackle this for self study or even calculative reference without "advanced" calculus (in my definition, analysis) PLUS a good course in analytic geometry first. Although this is packed with AG, it does not start by teaching AG-- the geometry knowledge is assumed, and we're then treated to an astonishing adventure of detailed APPLICATIONS of geometry to nearly every aspect of physics, including numerous cutting edge and intractable problems. There also are NUMEROUS engineering applications examples, blending physics, engineering and geometry in a way no other text even attempts.
I've long felt that some pundits who tease the Greeks for seeing everything as geometric would someday eat their words. Well.. wow. This volume clearly demonstrates how much what comes round goes round. OK, looking at physical spheres is not the same as spacetime curvature spheres, let alone "field" geometry that isn't even a physical geometry, but the geometry of a vector bundle!
So, to be honest, if you see the word "introduction" in this text's title, and think you'll be guided through the UNDERSTANDING of Lie algebras, matrix calculus, Yang-Mills and other gauges via geometry-- be careful. "Introduction" as I read it after reading this text means intro to the APPLICATION and CALCULATION techniques available to someone already well grounded in analytic geometry. Don't get me wrong, the author is simply amazing, as were the very successful first two editions, in carefully explaining many neglected applications of AG to physics, but this book would be 3,000 pages if we actually expected it to "introduce" every notation. So, it does blast right off assuming a good base in analytic geometry, and a fair base in physics.
One really cool dimension for self-study-- the author is obviously first a mathematician, and within that a geometer, so the pedagogic artifact from older days of showing NUMEROUS diagrams and illustrations made its way into this fine text. Even if I weigh the overall presentation as more computational that didactic, the illustrations themselves bely that evaluation-- each one gives one of those "aha" moments. The author also does take the time to explain the WHY of certain formula elements so you really "get" them. For example, if we're given an element where x^(exp polynomial) = b*(expression), the author WILL digress enough to remind us that b is acting as a proportionality constant. I find this really helpful as a way to generalize the lesson learned, otherwise we're just rote memorizing or referring back to a process we're not really getting! Highly recommended with the caveats mentioned about brushing up on your analytic/ differential geometry.
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4 of 7 people found the following review helpful.
Topics are great. Notation and typesetting could be improved
By givoLtaqe
Topics are great. Notation and typesetting could be improved, but since this is already the 3rd edition, I can only say I don't understand the author/publisher's decision of insisting on using unconventional notations every now and then and such ugly typesetting.
7 of 12 people found the following review helpful.
Great book!
By Norm Franzen
The Geometry of Physics is written in a very modern style and with a great choice of topics. A mathematician can enjoy this book even though it is mathematical physics. The mathematics is presented in very nice form.
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