Sine-Gordon type field in spacetime of arbitrary dimension. II: Stochastic quantization

Using the theory of Dirichlet forms we prove the existence of a distribution-valued diffusion process such that the Nelson measure of a field with bounded interaction density is its invariant probability measure. A Langevin equation in mathematically correct form is formulated which is satisfied by the process. The drift term of the equation is interpreted as a renormalized Euclidean current operator.