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Cambridge Monographs on Mathematical Physics
Differential Geometry, Gauge Theories, and Gravity
Using a self-contained and concise treatment of modern differential geometry, this book will be of great interest to graduate students and researchers in applied mathematics or theoretical physics working in field theory, particle physics, or general relativity. The authors begin with an elementary presentation of differential forms. This formalism is then used to discuss physical examples, followed by a generalization of the mathematics and physics presented to manifolds. The book emphasizes the applications of differential geometry concerned with gauge theories in particle physics and general relativity. Topics discussed include Yang-Mills theories, gravity, fiber bundles, monopoles, instantons, spinors, and anomalies.
248 pages, Paperback
First published January 1, 1978
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Displaying 1 - 3 of 3 reviews
March 6, 2023
Only read until Chapter 7 just for "quality check", since I am selling off the book due to moving for my next job.
This book does require some background in general relativity and classical field theory, perhaps also Lie algebra and Lie groups for readers to benefit the most. It's also quite technical but very well-written and articulate. What I really like about this book, however, is the "caveats": for example, it emphasized in Section 4.7 that gauge group is not the same as the Lie group associated to the gauge theory because the former is infinite-dimensional. In Chapter 5 (Section 5) it also mentioned the (important) fact that coordinate transformations are -not- diffeomorphisms; the latter is a non-Abelian infinite-dimensional group and is globally defined. The former cannot be due to coordinate singularities. Very concise and precise. Chapter 7 (Section 6) also mentions briefly why parallelizability is relevant in physical settings.
I would read this properly if I were to still work on this stuff (I am moving towards quantum information theory and less relativity now), but now I know I can recommend this to people.
This book does require some background in general relativity and classical field theory, perhaps also Lie algebra and Lie groups for readers to benefit the most. It's also quite technical but very well-written and articulate. What I really like about this book, however, is the "caveats": for example, it emphasized in Section 4.7 that gauge group is not the same as the Lie group associated to the gauge theory because the former is infinite-dimensional. In Chapter 5 (Section 5) it also mentioned the (important) fact that coordinate transformations are -not- diffeomorphisms; the latter is a non-Abelian infinite-dimensional group and is globally defined. The former cannot be due to coordinate singularities. Very concise and precise. Chapter 7 (Section 6) also mentions briefly why parallelizability is relevant in physical settings.
I would read this properly if I were to still work on this stuff (I am moving towards quantum information theory and less relativity now), but now I know I can recommend this to people.
July 18, 2017
This is a really really remarkable book. It covers Stora's algorithm and has a nice discussion of anomalies.
October 9, 2022
This book never explains anything. Harder than Jackson's E&M.
Displaying 1 - 3 of 3 reviews