Vacuum and thermal fluctuation energies of a soliton at finite temperatures

TL;DR

This paper investigates the vacuum and thermal fluctuation energies of a soliton at finite temperatures, employing renormalization techniques and numerical analysis to understand their behavior.

Contribution

It introduces a method to calculate and analyze vacuum and thermal energies of solitons at finite temperatures using a consistent renormalization scheme.

Findings

Vacuum energy is computed by summing discrete and continuum spectra.

Renormalization removes divergences at zero temperature.

Numerical results reveal temperature-dependent energy behaviors.

Abstract

We have studied the vacuum and thermal fluctuation energies of a soliton at finite temperatures. First the vacuum energy coming from the Dirac sea is calculated by a summation of the discrete and continuum energy spectrum of the Dirac equation in the background field of a soliton. And all the divergences are removed by the same renormalization scheme at zero temperature. Then the vacuum energy and thermal fluctuation energy at finite temperatures in a temperature dependent soliton background are calculated. And the numerical results are analyzed and discussed.