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Can anyone give me references where I would see a detailed exposition of how to translate gauge field theory as known to physicists into the language of connections. I am looking for a detailed exposition on the mathematical formulation of Yang-Mills field theory. Something which might also give an exposition about Chern-Simons theory and the related whole bag of what get called "topological actions"

I had read a nice long discussion on the geometrical formulation of gauge field theory in a post at Terence Tao's blog namely this article and also probably something on Secret Blogging Seminar (but I can't locate that link)

Along similar lines I had seen a very old book by Atiyah and Hitchin on this.

I would like to know what books/expository papers on this are read by graduate students today when they try entering this field?

Also advanced references on the topic would also be helpful.

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3 Answers 3

up vote 3 down vote accepted

Geometry, Topology, and Physics by Nakahara

Classical Theory of Gauge Fields by Rubakov

Modern Geometry, Part 2 by Dubrovin, Fomenko, and Novikov

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The books that I liked by far the most are the two volumes on Topology, Geometry and Gauge Fields by Gregory Naber. It has a very nice introductory chapter which tells you why one should care about connection and then starts topology from the scratch. The second book ends with a short introduction to Seiberg-Witten gauge theory (to be found on his homepage, "Introduction to Donaldson and Seiberg-Witten Theories").

I also enjoyed John Morgan's lectures on Gauge theory in the book "Gauge theory and topology of four-manifolds".

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I second the suggestion of Naber's book. Physicist friends of mine have found it very helpful in passing between physical language and mathematical language. –  Joel Fine Jan 11 '10 at 14:05
    
I had read through Naber's volume 1 during my undergrad and had found it exciting and insightful. Haven't seen the volume 2. Given your recommendation I think I should take a look then. –  Anirbit Jan 11 '10 at 16:43
    
Can you also provide a link to the home-page from where you said that the book is available? I did quite a few Google searches but nothing came up except the flipkart and amazon and google books link for the book. –  Anirbit Jan 11 '10 at 16:53
    
Sorry for the unclarity: Not the book is available on his homepage, only the appendix to Seiberg-Witten Gauge theory. –  Alexander Noll Jan 11 '10 at 17:26
    
Thanks for the clarification. But your link doesn't work. Can you kindly correct it? –  Anirbit Jan 12 '10 at 8:44
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I found K. Moriyasu's An Elementary Primer for Gauge Theory a helpful expository introduction.

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