Emerging Translational Variance: Vacuum Polarization Energy of the ${\varphi }^6$ kink

Abstract

We propose an efficient method to compute the vacuum polarization energy of static field configurations that do not allow a decomposition into symmetric and anti-symmetric channels in one space dimension. In particular we compute the vacuum polarization energy of the kink soliton in the ${\varphi }^6$ model. We link the dependence of this energy on the position of the center of the soliton to the different masses of the quantum fluctuations at negative and positive spatial infinity.

arXiv comment13 pages, changes made to match journal version (including title)

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• Collisions of kinks in deformed ${\phi }^4$ and ${\phi }^6$ models
• Quantum Instabilities of Solitons
• The Two-Loop ${\varphi }^4$ Kink Mass
• Quantum Corrections to Solitons in the ${\Phi }^8$ Model
• Kink scattering in the presence of geometric constrictions
• Geometrically constrained sine-Gordon field: BPS solitons and their collisions
• Phonons scattering off discrete asymmetric solitons in the absence of a Peierls-Nabarro potential
• Scattering of kinks in scalar-field models with higher-order self-interactions