I'm a senior undergraduate student studying differential geometry. I have experience with smooth manifolds, some elementary theory of Lie groups, and a little multi-linear algebra. I understand this is all very "par for the course" for a first exposure to any serious amount of differential geometry.
It's come to my attention that a lot of the material I've encountered has interesting applications to mathematical physics, a discipline I know very little about. Since physics is interesting to me, I would like to dabble into these applications a little bit. So the function of this post is two-fold.
First, what kind of background material is necessary to really understand the applications of geometry to physics? The last real course in physics I had was at the Newtonian level. I've done some reading past that in fluids, and a little bit of electromagnetism, but that was just light reading.
Of course, with the background material covered, the next question is for a solid reference in physics that I could use. I find electricity and magnetism interesting and fluid dynamics interesting. I'm not so interested in mechanics, but if it's necessary I learn about it in more detail first, that's fine by me. I understand that field theories of any type eventually run up against quantum mechanics, which is also an area of thought I know relatively little about from a rigorous perspective.
I suppose I prefer a reference which is not too long, because I'll only have about 8 weeks between semesters to study from. If it isn't possible to get a good understanding in that time, then I can always continue with the material in the summer time. I also prefer an approach which is more geometric than analytic, if possible.