The Chern-Simons function on the space of connections, mod the gauge transformations, on a 3-manifold can be defined by an integral. I study mathematics as profession, so I want to know what is the significance (i.e. meaning, intuition, etc) of space of connections in physics. It makes sense mathematically, it is just a manifold. But what is this space really and what does integration on it mean in physics?

This post imported from StackExchange Physics at 2015-09-23 09:29 (UTC), posted by SE-user nikita