Gilkey-de Witt heat kernel expansion and zero modes

TL;DR

This paper generalizes the Gilkey-de Witt heat kernel expansion to accurately estimate the heat trace of certain differential operators, enabling effective computation of quantum corrections in models with unknown spectra.

Contribution

It introduces a modified heat kernel expansion method for operators with zero modes, improving the estimation of quantum effects in field theory models.

Findings

Effective computation of one-loop kink mass shifts.

Application to models with unknown fluctuation spectra.

Enhanced accuracy in heat trace estimations.

Abstract

In this paper we propose a generalization of the Gilkey-de Witt heat kernel expansion, designed to provide us with a precise estimation of the heat trace of non-negative Schroedinger type differential operators with non-trivial kernel over all the domain of its "inverse temperature" variable. We apply this modified approach to compute effectively the one-loop kink mass shift for some models whose kink fluctuation operator spectrum is unknown and the only alternative to estimate this magnitude is the use of the heat kernel expansion techniques.