Exact computation of loop averages in two-dimensional Yang-Mills theory

We present an explicit algorithm that allows the exact computation of all nonlocal gauge-invariant correlation functions in two-dimensional Yang-Mills theory. Explicit expressions are given for the expectation value of entangled loop operators and their products in the U(N) theory with arbitrary N.Using these results we show that the Schwinger-Dyson equation for loops holds without singularities in the continuum, and we verify the factorizability of the correlation functions in the N-->∞ limit. A non-Abelian version of Stokes's theorem which is used in the calculations is derived for an arbitrary number of dimensions.