Local Casimir Energy For Solitons

TL;DR

This paper introduces a local regularization method for calculating the Casimir energy density of solitons, revealing new insights into the anomalous and non-anomalous contributions, especially in supersymmetric models.

Contribution

It presents a novel local mode regularization technique and demonstrates phase space factorization for reflectionless potentials, aligning energy density calculations with known central charge densities.

Findings

Mode density equality yields anomalous energy density

Phase space factorization simplifies non-anomalous energy density

Agreement with central charge density in supersymmetric models

Abstract

Direct calculation of the one-loop contributions to the energy density of bosonic and supersymmetric phi-to-the-fourth kinks exhibits: (1) Local mode regularization. Requiring the mode density in the kink and the trivial sectors to be equal at each point in space yields the anomalous part of the energy density. (2) Phase space factorization. A striking position-momentum factorization for reflectionless potentials gives the non-anomalous energy density a simple relation to that for the bound state. For the supersymmetric kink, our expression for the energy density (both the anomalous and non-anomalous parts) agrees with the published central charge density, whose anomalous part we also compute directly by point-splitting regularization. Finally we show that, for a scalar field with arbitrary scalar background potential in one space dimension, point-splitting regularization implies local mode regularization of the Casimir energy density.