Wilson Loops in Two-Dimensional Space-Time Regarded as White Noise

Wilson loops are formally defined as ei∮C A(x) dx where C is a closed curve and A is the electromagnetic Vector potential. In this paper the case of two-dimensional Euclidean space-time is investigated. A satisfies the equation ∂A = F, F being generalized white noise. A rigorous definition of Wilson loops is given and the N-loop Schwinger functions, which are shown to satisfy Seiler′s axioms, are explicitly calculated.