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

[ChrisVer]

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

 

[Fredrik]

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.

 

[MathematicalPhysicist]

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.

 

[Fredrik]

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.

 

[MathematicalPhysicist]

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).