Statistical linearizations for stochastically quantized fields

TL;DR

This paper applies statistical linearization to stochastically quantized fields at finite temperature, deriving implicit equations for self-energy that align with Dyson-Schwinger equations, and demonstrates this with three quantum models.

Contribution

It introduces a novel application of statistical linearization to quantum field theories, connecting it with established diagrammatic summations and handling divergences via Ramanujan summation.

Findings

Derived implicit equations for self-energy in quantum fields

Connected linearization method with Dyson-Schwinger equations

Successfully applied to three quantum models

Abstract

The statistical linearization method known in nonlinear mechanics and random vibrations theory has been applied to stochastically quantized fields in finite temperature. It has been shown that even in its simplest form the method yields convenient implicit equations for the self-energy, equivalent to the Dyson-Schwinger equations resulting from the summation of infinite number of perturbative diagrams. Three examples have been provided: the quantum anharmonic oscillator, the scalar $\phi^{4}$ theory in three spatial dimension, and the Bose-Hubbard model. The Ramanujan summation has been used to deal with divergent integrals and series.