Quantum corrections to static solutions of phi-in-quadro and Sin-Gordon models via generalized zeta-function

TL;DR

This paper introduces a generalized algebraic method using zeta-functions to compute quantum corrections to classical solutions like kinks and periodic solutions in phi-in-quadro and Sin-Gordon models across various dimensions.

Contribution

It presents a novel algebraic approach employing generalized zeta-functions and Green functions for calculating quantum corrections in classical field models.

Findings

Quantum corrections to classical solutions are computed in arbitrary dimensions.

Green functions for soliton potentials are constructed using Laplace transformation.

The method effectively evaluates quantum corrections to mass in the quasiclassical approximation.

Abstract

A general algebraic method of quantum corrections evaluation is presented. Quantum corrections to a few classical solutions (kinks and periodic) of Ginzburg-Landau (phi-in-quadro) and Sin-Gordon models are calculated in arbitrary dimensions. The Green function for heat equation with a soliton potential is constructed by means of Laplace transformation theory and Hermit equation for the Green function transform. The generalized zeta-function is used to evaluate the functional integral and quantum corrections to mass in quasiclassical approximation.