The Moduli Space of Flat Connections on Oriented Surfaces with Boundary

A 2-form is constructed on the space of connections on a principal bundle over an oriented surface with boundary. This induces a symplectic structure for the moduli space of flat connections with boundary holonomies lying in prescribed conjugacy classes. The Yang–Mills quantum field measure is described for this situation. This measure converges to the normalized symplectic volume measure in the “classical” limit.