On the stochastic quantization of field theory (Q1073452)

We give a rigorous construction of a stochastic continuum \(P(\phi)_ 2\) model in finite Euclidean space-time volume. It is obtained by a weak solution of a non-linear stochastic differential equation in a space of distributions. The resulting Markov process has continuous sample paths, and is ergodic with the finite volume Euclidean \(P(\phi)_ 2\) measure as its unique invariant measure. The procedure may be called stochastic field quantization.