I'm looking for a textbook or set of lecture notes on gauge theory for mathematicians that assumes only minimal background in physics. I'd prefer a text that uses more sophisticated mathematical concepts like principal bundles and connections, and categorical language whenever convenient.
I have been writing something in this direction in section 1 of the book Differential cohomology in a Cohesive topos (pdf). Have a look, just focus on section 1 and ignore the remaining sections on first reading.
The survey-part is presently also appearing as a series on PhysicsForums. See at Higher prequantum geometry I, II, III, IV, V and Examples of Prequantum Field Theories I -- Gauge fields, II -- Higher gauge fields.
One less well-known but great reference are the classical field theory notes by Deligne and Freed in the '99 IAS lectures. Some good things about them
- Very elegant treatment written for mathematicians
- Begins with a nice discussion of ordinary classical mechanics using principal bundles and connections
- Useful comments on supersymmetric gauge theories throughout.