Which Book is Best for Studying Fiber Bundles in Yang-Mills Gauge Theories?

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Discussion Overview

The discussion revolves around recommendations for books on fiber bundles, particularly in the context of Yang-Mills gauge theories and differential geometry. Participants share their experiences with various texts and express their preferences based on comprehensibility and rigor.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion with their professor's advanced differential geometry book and seeks comprehensible sources for studying fiber bundles.
  • Another participant recommends Isham's book "Differential Geometry for Physicists" as a good starting point, though notes it may not cover everything needed.
  • A suggestion is made for Nakahara's book, highlighting its suitability for physicists who prefer less emphasis on rigorous proofs, although one participant has reservations about its lack of mathematical rigor.
  • One participant shares a negative experience with Nakahara, suggesting their opinion may be outdated due to their prior lack of knowledge in differential geometry.
  • Several other books are mentioned as potential resources, including Frankel, Fecko, Baez & Muniain, and works by John M. Lee, with one participant emphasizing the importance of rigor in their mathematical studies.
  • Another participant mentions Nash's book as an additional option, reiterating a preference for rigorous mathematical treatment.
  • A comparison is made between the coverage of topics in Nakahara and Hatcher's book, with the former being noted for its brevity.

Areas of Agreement / Disagreement

Participants express differing opinions on the suitability and rigor of various books, indicating that no consensus exists on the best resource for studying fiber bundles in this context.

Contextual Notes

Some participants' recommendations depend on their personal experiences and preferences for mathematical rigor versus applied approaches, which may not align with everyone's learning style.

ChrisVer
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I would like a good source from which I can study fiber bundles (mainly their application in Yang-Mills gauge theories, but also in differential geometry)... I tried to study them from the advanced differential geometry (note)book of 1 of my professors but it was a mess and it confused me even more.
If you studied it from some book and you find it comprehensible, please let me know
 
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Isham's book Differential Geometry for Physicists is a very good place to start, but it doesn't quite take you all the way there.
 
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Perhaps Nakahara is suitable for your goal:

https://www.amazon.com/dp/0750306068/?tag=pfamazon01-20

I haven't read it as it doesn't provide proofs to most of the theorems that are stated there.

It seems suitable for physicists who don't want to be bogged down with all the tedious details of the proofs of theorems.
 
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I tried to study some stuff in Nakahara a long time ago, and I didn't like it. But it was a long time ago, probably before I had even studied differential geometry. So you probably shouldn't give that comment too much weight. (Edit: I mean my comment in the preceding sentence, not the other guy's comment in the preceding post).

If I ever find the time to refresh my memory about the things in Isham, and then continue along that path, I think I will try Frankel, Fecko or Baez & Muniain, maybe all of them.

Also, the books by John M. Lee are definitely the best place to study the basics of differential geometry.
 
Well, I recommended Nakahara not because of its mathematical rigor, but because of its applied nature to physics.

There's also Nash's book.

I myself prefer my math to be as rigorous as possible so I don't believe that I'll use these books.

I mean from the table of contents you can be self assured that the coverage is short and to the point, I mean Homotopy and Homology in Nakahara's is discussed in less than 200 pages, and in Hatcher's it's like 400-500 pages. (It's my recollection from my memory which may be wrong).
 

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