Abstract
The quantum field (Euclidean) measure for gauge fields aver compact surfaces, possibly with boundary, with simply-connected compact gauge groups is constructed using a conditioned Gaussian measure on a non-linear space. An explicit formula, involving certain topological invariants for surfaces and curves, is derived which gives expectation values for a very general class of Wilson loop configurations. It is shown that these values are invariant under area-preserving homeomorphisms of the surface.
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