A Variational Approach to Excited Fermions on Kinks

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.