The Yang-Mills Measure for the Two Sphere.

The Yang-Mills measure for gauge fields over the two-sphere is constructed using a conditioned white-noise process. Parallel transport according to stochastic connections is studied in this setting using stochastic differential equations. Expectations of Wilson loop variables are computed and results are proved which may be interpreted as the invariance of the Yang-Mills measure under area-preserving diffeomorphisms of the sphere. A limiting behavior of the measure under scaling of the Yang-Mills action functional is studied.