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.
Best Answer
Geometry, Topology, and Physics by Nakahara
Classical Theory of Gauge Fields by Rubakov
Modern Geometry, Part 2 by Dubrovin, Fomenko, and Novikov