Vacuum polarization energy of the Shifman-Voloshin soliton

TL;DR

This paper calculates the vacuum polarization energy of a two-field soliton model in one dimension, revealing that quantum effects generally destabilize the soliton unless the fields have equal masses, where the model simplifies.

Contribution

It introduces spectral methods to compute vacuum polarization energy in a two-field soliton model, extending the conventional $^4$ kink analysis.

Findings

Vacuum polarization energy tends to destabilize the soliton.

Equal masses in the two fields lead to a stable configuration.

The model reduces to two independent $^4$ models when masses are equal.

Abstract

We compute the vacuum polarization energy of soliton configurations in a model with two scalar fields in one space dimension using spectral methods. The second field represents an extension of the conventional $\phi^4$ kink soliton model. We find that the vacuum polarization energy destabilizes the soliton except when the fields have identical masses. In that case the model is equivalent to two independent $\phi^4$ models.