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A Variational Approach to Excited Fermions on Kinks
Version 1
: Received: 27 November 2023 / Approved: 28 November 2023 / Online: 29 November 2023 (09:47:58 CET)
A peer-reviewed article of this Preprint also exists.
Weigel, H.; Saadatmand, D. A Variational Approach to Excited Fermions on Kinks. Universe 2024, 10, 13. Weigel, H.; Saadatmand, D. A Variational Approach to Excited Fermions on Kinks. Universe 2024, 10, 13.
Abstract
We study the back-reaction of fermion fields on the kink solution in one space and one time dimension. We employ a variational procedure to determine an upper limit for the minimum of the total energy. This energy has three contributions: the classical kink energy, the energy of valence fermions and the fermion vacuum polarization energy. The latter arises from the interaction of the kink with the Dirac sea and is required for consistency of the semi-classical expansion for the fermions. Earlier studies only considered the valence part and observed a substantial back-reaction. This was reflected by a sizable distortion of the kink profile. We find that this distortion is strongly mitigated when the Dirac sea is properly accounted for. As a result the back-reaction merely produces a slight squeeze or stretch of the kink profile.
Keywords
Kinks; fermions; Dirac sea; vacuum polarization energies; variational methods
Subject
Physical Sciences, Particle and Field Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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