Yang-Mills theory in the Minkowski plane

Question

It is well-known that quantum Yang-Mills theory in the cylinder is exactly solvable. But what happens for Yang-Mills in the 2D Minkowski plane? There should be something like a limit where the radius goes to infinity but I have never seen this discussed. Are there papers discussing this limit? If not, what is the reason?

Comments

The difference may be in the boundary conditions. Whether there are the reflected waves or  the outgoing waves are absorbed; that is what makes a difference, in my humble opinion.