Quantum Mass Correction of Solitons in (1+1)D via Numerical Methods

TL;DR

This paper develops numerical methods to compute quantum mass corrections for solitons in (1+1)D field theories, enabling analysis of non-integrable models and providing detailed mode-by-mode calculations for specific models.

Contribution

It introduces a trace formula-based numerical approach to calculate quantum mass corrections for solitons, applicable to non-integrable models like the $ ext{phi}^4$ kink.

Findings

Numerical computation of quantum corrections for Sine-Gordon and $ ext{phi}^4$ solitons.

Mode-by-mode analysis reveals dominant contributions from lowest modes.

Method provides a practical tool for studying quantum effects in non-integrable solitonic models.

Abstract

We show how to calculate the quantum mass correction to (1+1)D solitonic field theories using numerical methods. This is essential if we want to find the corrections to non-integrable models. We start with a review of the standard derivation of the first order quantum correction. Then, we re-derive a trace formula which allows us to compute the mass correction mode by mode. Specifically, we are interested in the extent to which the lowest modes from both, the soliton and the vacuum, sectors give the leading contribution. We apply the technique to both the Sine-Gordon and the $\phi^4$-kink model. Then, we compute all the modes numerically and hence the first order quantum contribution to the mass of the Sine-Gordon and $\phi^4$ soliton.