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Two dimensional Yang-Mills theory via stochastic differential equations. (English) Zbl 0698.60047

Summary: The equation of parallel transport is given meaning in the quantized two dimensional Euclidean Yang-Mills theory by interpreting it as a stochastic differential equation in the complete axial gauge. The expectation of products of Wilson loops is evaluated using the stochastic differential calculus and a method of Bralic. Euclidean invariance of the theory is proven.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
81P20 Stochastic mechanics (including stochastic electrodynamics)
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