Local Casimir Energy For Solitons

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.

18 pages. Numerous new clarifications and additions, of which the most important may be the direct derivation of local mode regularization from point-splitting regularization for the bosonic kink in 1+1 dimensions

References in corpus (3)

• Mode regularization of the susy sphaleron and kink: zero modes and discrete gauge symmetry
• Quantization of supersymmetric solitons
• Clash of discrete symmetries for the supersymmetric kink on a circle

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• Well-Defined Quantum Soliton Masses Without Supersymmetry
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• Casimir Energy for a Coupled Fermion-Kink System and its stability
• A Renormalized perturbation theory for problems with nontrivial boundary conditions or backgrounds in two space-time dimensions
• The semiclassical energy density of kinks and solitons
• Clash of discrete symmetries for the supersymmetric kink on a circle
• An Investigation of the Casimir Energy for a Fermion Coupled to the Sine-Gordon Soliton with Parity Decomposition
• One-loop results for kink and domain wall profiles at zero and finite temperature
• Comment on `One Loop Renormalization of Soliton Quantum Mass Corrections in 1+1 Dimensional Scalar Field Theory Models' (Phys. Lett. B542 (2002) 282 [hep-th/0206047])
• One-loop quantum correction to the mass of the supersymmetric Kink in (1 + 1) dimensions using the exact spectra and the phase shifts
• Perturbative Quantum Corrections to the Supersymmetric CP^1 Kink with Twisted Mass
• Quantum corrections to the mass and central charge of solitons in 1+1 dimensions
• On the nature of the anomalies in the supersymmetric kink
• The ${\varphi }^4$ Kink Mass at Two Loops
• Vacuum Polarization and Casimir Energy of a Dirac Field Induced by a Scalar Potential in One Spatial Dimension