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Gauge theory in physics and mathematics refers to a field theory whose fields include principal bundles with connection.

11 votes
4 answers
2k views

Literature for gauge field theory on the lattice in geometrical formulation

I have found an article by Huebschmann, Rudolph and Schmidt about "A Gauge Model for Quantum Mechanics on a Stratified Space" and I am very interested in this subject, but I don't have any background …
34 votes
6 answers
4k views

Is symplectic reduction interesting from a physical point of view?

Do you think that symplectic reduction (Marsden Weinstein reduction) is interesting from a physical point of view? If so, why? Does it give you some new physical insights? There are some possible ans …
1 vote
2 answers
574 views

Reference for some elementary facts about principal bundles

Let $(P,\pi,B,G)$ be a principal bundle with total space $P$, base $B$, projection $\pi$ and structure group $G$. Now I am searching for a good reference (with proofs) for the following facts: 1) T …
1 vote

module of sections of the horizontal bundle

For those who are interested I give here a slightly more detailed version of Michael's answer. First note that $T\pi|_{HP} \colon HP \to TB$ is a vector bundle map covering $\pi \colon P \to B$ and a …
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1 vote
2 answers
655 views

module of sections of the horizontal bundle

Some times ago I posted this question here. There I carelessly assumed that if you have a set of sections of a vector bundle which span every fiber pointwise, they also generate the module of smooth s …