Excited fermions on kinks and the Dirac sea

TL;DR

This paper investigates quantum effects of kink solitons coupled with an excited fermion, revealing that vacuum polarization energy significantly impacts the stability and energy balance of these solutions.

Contribution

It introduces a self-consistent approach to compute the Dirac sea energy for kink solitons with an excited fermion, highlighting the importance of vacuum polarization effects.

Findings

Vacuum polarization energy is substantial and often exceeds the energy gained from binding the fermion.

The energies of the bound fermion level and the Dirac sea should be treated equally in semi-classical calculations.

Quantum effects significantly influence the stability of kink solitons with excited fermions.

Abstract

We study quantum effects of recently discovered kink solitons which are constructed self-consistently by coupling to a single, excited fermion bound state. Our studies are based on the observation that in a semi-classical expansion the energies of this single level and of the Dirac sea should be treated equally. For these kink solutions we compute the energy of the Dirac sea as the fermion vacuum polarization energy. We find it to be substantial and to typically outweigh the energy gain from binding the single level.