Nonlocality and stochastic quantization of field theory

Abstract

The concept of nonlocality is introduced into physics by means of a stochastic context using Langevin and Schwinger-Dyson techniques. This allows us to reformulate the finite theory of quantum fields, free from ultraviolet divergences, based on the stochastic quantization method with nonlocal regulators. As a nonlocal regulator we choose any entire analytic function in the momentum space, which guarantees that our regularization method for any theory of interest does not violate basic physical principles such as unitarity, causality, and gauge invariance of the theory. Here we present the regularization scheme for scalar, gauge, and scalar electrodynamic theories. Our mathematical prescription is similar to the continuum regularization method of quantum field theory with meromorphic regulators investigated by Bern and his team.