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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 ...


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 ...

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