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Nov 5 at 1:28 comment added b0bgary OK thankyou, I had been reading about the Gribov obstruction just before this. Suppose then that I'm considering a boundary of some finite region in a slice of $\mathbb{R}^4$. I only care about the value of $A$ on this closed curve, rather than all of $\mathbb{R}^4$. I understand that I can't have a global section, but what can I say about $A$ in this case? Is there a well-defined splitting on this submanifold?
Nov 1 at 11:03 comment added Branimir Ćaćić Gribov ambiguity is an issue even for abelian Yang–Mills gauge theory over compact manifolds at least: in the case of $U(1)$-gauge theory, you get Gribov ambiguity iff the first Betti number is non-zero.
S Nov 1 at 4:51 review First answers
Nov 1 at 8:39
S Nov 1 at 4:51 history answered Budjum CC BY-SA 4.0