QUANTUM YANG-MILLS ON THE 2-SPHERE

We obtain the quantum expectations of gauge-invariant functions of the connection on a principal G=SU(N) bundle over S2. We show that the space A/gm of connections modulo gauge transformations which are the identity at one point is itself a principal bundle over ΩG, based loops in the symmetry group. The fiber in A/gm is an affine linear space. Quantum expectations are iterated path integrals first over this fiber then over ΩG, each with respect to the push-forward to A/gm of the measure s-S(A)DA. S(A) denotes the Yang-Mills action on A. There is a global section of A/gm on which the first integral is a Gaussian. The resulting measure on ΩG is the conditional Wiener measure. We explicitly compute the expectations of a special class of Wilson loops. © 1990 Springer-Verlag.