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I was searching for introductions to current mathematics related to gauge theories.

Can someone suggest some good references?

E.g.

Topics in Physical Mathematics by K. Marathe

edited Nov 25 2011 at 14:01

asked Nov 25 2011 at 13:18

Sadiq Ahmed
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Since you are asking for "mathematics related to gauge theories" I am assuming that you mean "gauge theory" in the context of physics. In mathematics, the term "gauge theory" is a well-defined subfield of differential geometry: the study of connections on vector bundles, usually with special properties, and their associated moduli spaces. This is a huge area of current mathematical research. Some of it is physics inspired, but certainly not all of it. – Spiro Karigiannis Nov 25 2011 at 14:18

If I'm not mistaken "gauge field" in physics is equivalent to "connections on vector bundles" in maths. - In the context of your comment, I mean 'gauge theory' in the context of maths. – Sadiq Ahmed Nov 25 2011 at 14:28

(ie. current pure mathematics inspired by / from "gauge (field) theory" in physics) – Sadiq Ahmed Nov 25 2011 at 14:30

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This question is awfully broad. Are you looking for introductions to areas like Donaldson theory or Seiberg-Witten theory? – S. Carnahan♦ Nov 26 2011 at 3:48

Jon · Answer 1 · 2011-11-25 14:04:09Z UTC

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See these

Quantum Fields and Strings: A Course for Mathematicians

Quantum Field Theory for Mathematicians

and, as a physicist, I would also add Faddeev and Slavnov

Gauge Fields: An Introduction To Quantum Theory

answered Nov 25 2011 at 14:04

Jon
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Igor Khavkine · Answer 2 · 2011-11-25 17:55:01Z UTC

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Kevin Costello, Renormalization and Effective Field Theory

Frédéric Paugam, Towards the mathematics of quantum field theory

answered Nov 25 2011 at 17:55

Igor Khavkine
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Reference request: Introductions to current mathematics derived from / related to gauge theories

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