Investigation of Green Functions and the Parisi-Wu Quantization Method in Background Stochastic Fields

Abstract

In this review we present variational and stochastic method of evaluating functional integrals and quantization of different fields (scalar, electromagnetic and Yang-Mills gauge ones). These methods are applied to the study of the asymptotic behavior of the scalar particle Green functions in stochastic fields and to the construction of a finite quantum field theory by means of the nonlocal white noise-like background stochastic fields in the scheme due to Parisi and Wu. In our mathematical prescription the white noise-like field plays a double role, it controls the quantum behavior of the theory and at the same time it carries nonlocality in stochastic Langevin-type equations. We also introduce stochasticity of the space-time metric in the context of stochastic background field and discuss its consequences.