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.


Geometry, Topology, and Physics by Nakahara

Classical Theory of Gauge Fields by Rubakov

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


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".

  • $\begingroup$ 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. $\endgroup$
    – Joel Fine
    Jan 11 '10 at 14:05
  • $\begingroup$ 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. $\endgroup$
    – Anirbit
    Jan 11 '10 at 16:43
  • $\begingroup$ 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. $\endgroup$
    – Anirbit
    Jan 11 '10 at 16:53
  • $\begingroup$ Sorry for the unclarity: Not the book is available on his homepage, only the appendix to Seiberg-Witten Gauge theory. $\endgroup$ Jan 11 '10 at 17:26
  • $\begingroup$ Thanks for the clarification. But your link doesn't work. Can you kindly correct it? $\endgroup$
    – Anirbit
    Jan 12 '10 at 8:44

I found K. Moriyasu's An Elementary Primer for Gauge Theory a helpful expository introduction.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.