Regularization in the Minkowski stochastic quantization scheme. Scalar model and QED

Using the functional method Fukuda and Higurashi we show that, for a markovian stochastic regularization, there exists an equilibrium limit of the regularized generating functional in Minkowski stochastic quantization of scalar theory. The method is also applied to define Minkowski stochastic quantization of QED in the covariant α-gauge. It is pointed out that the present perturbation scheme needs Pauli-Villars regularization performed at the Langevin level. (orig.)