  Stochastic quantization provides a connection between quantum field theory
and statistical mechanics, with applications especially in gauge field
theories. Euclidean quantum field theory is viewed as the equilibrium limit of
a statistical system coupled to a thermal reservoir. Nonlinear phenomena in
stochastic quantization arise when employing nonlinear Brownian motion as an
underlying stochastic process. We discuss a novel formulation of the Higgs
mechanism in QED.
