Differential Geometry, Gauge Theories, and Gravity (Cambridge Monographs on Mathematical Physics) by M. Göckeler (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “…a very beautifully and elegantly written introduction to those areas of modern differential geometry that either now play, or presumably will play, a role in particle physics and general relativity.” SIAM Review

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book is very hard to understand. It looks like authors are really lazy at explaining things. It’s even harder than J D Jackson’s ‘Classical Electrodynamics’.

⭐This text belongs with ‘Analysis, Manifolds and Physics’ by Choquet-Bruhat et al. and other contemporary classics in mathematical physics. Ryder’s ‘Quantum Field Theory’ and the books by Nash and Sen would also make the list — texts which take one into the heart of the matter in a lucid, logical progression through the essential ideas.

⭐This text, while lacking in rigour and detail, is an ideal supplement for self-study or lectures on modern mathematical methods in physics. In fact, it is precisely its lack of detail that allows it to act as the yin to the yang of other, weightier texts. Most books on this subject obscure the big picture behind their equations, reducing pleasant geometry to the grimy level of analysis. No such crime is committed here, and the reader is much the better for it. To be sure, this is not a stand-alone text – to not delve into the details would only enter the reader into the false security of ignorance. However, it is most definitely a must-have book for anyone interested in modern physics and mathematics.Recommended texts to accompany this one are: 1) Geometry of Physics, Frankel 2) Intro to Lie Algebras & Rep. Th., Humphreys 3) Geometry, Topology,& Physics, Nakahara (another useful survey) 4) Spin Geometry, Lawson & Michelson

⭐THIS BOOK IS JUST ANOTHER EXAMPLE OF THE MANY PUBLICATIONS IN THIS SUBJECT MATTER THAT MISSES THE WHOLE POINT.

⭐This is a concise introduction to applications of differential geometry on some improtant topics in physics, such as gauge theories, gravity…etc. Despite its size (which is rather comfortable for readers who prefer less abstract definitions and theorems), nothing essential to the spirit of the topics has been missed, I personally think it sure is one of the excellent books on these subjects and am glad to recommand it to you all who love and want to discover the geometric aspects of physics!

⭐Un testo mediocre rispetto ai molti altri libri sulle basi geometriche delle teorie di gauge. Il testo si dilunga su argomenti di matematica che ogni studente di fisica teorica o di matematica può studiare su testi molto più chiari e più completi, mentre per gli aspetti fisici vi sono molte presentazioni di gran lunga più complete e più chiare.

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