One-loop correction to classical masses of quantum kink families

TL;DR

This paper calculates one-loop quantum corrections to the masses of kinks in a two-scalar field model, introducing a generalized formula and examining the impact on classical degeneracy.

Contribution

It develops a generalized DHN formula for potentials with reflection and analyzes quantum effects on kink degeneracy in a multi-field model.

Findings

Derived a generalized DHN formula for various potentials.

Showed the role of half-bound states in quantum mass corrections.

Addressed the quantum stability of classical kink degeneracy.

Abstract

One-loop corrections to kink masses in a family of (1+1)-dimensional field theoretical models with two real scalar fields are computed. A generalized DHN formula applicable to potentials with and without reflection is obtained. It is shown how half-bound states arising in the spectrum of the second order fluctuation operator for one-component topological kinks and the vacuum play a central r$\hat{{\rm o}}$le in the computation of the kink Casimir energy. The issue of whether or not the kink degeneracy exhibited by this family of models at the classical level survives one-loop quantum fluctuations is addressed.