Green functions of scalar particles in stochastic fields

A variational method of evaluating functional integrals is proposed. This method is used to investigate the asymptotic behavior of the scalar-particle Green functions in stochastic fields. The equations for the Green functions in Euclidean space in stochastic fields are written. The solutions of these equations are represented in the form of a functional integral and then they are averaged over Gaussian stochastic fields. The variational method formulated above is used to evaluate the asymptotic behavior of these Green functions. The following equations are considered in this paper: a stochastic contribution to the mass of a scalar particle, a gauge stochastic field, and a weak stochastic contribution to the flat metric of Euclidean space.