Stable branches of a solution for a fermion on domain wall

Abstract

We discuss the case when a fermion occupies an excited non-zero frequency level in the field of domain wall. We demonstrate that a solution exists for the coupling constant in the limited interval $1<g<g_{max}\approx 1.65$. We show that indeed there are different branches of stable solution for $g$ in this interval. The first one corresponds to a fermion located on the domain wall ($1<g<\sqrt[4]{2\pi }$). The second branch, which belongs to the interval $\sqrt[4]{2\pi }\le g\le g_{max}$, describes a polarized fermion off the domain wall. The third branch with $1<g<g_{max}$ describes an excited antifermion in the field of the domain wall.

15 pages, 7 figures, references added

References in corpus (4)

• Remarks on bell-shaped lumps: stability and fermionic modes
• Fermionic Zero Modes on Domain Walls
• Fermions on one or fewer Kinks
• On the interactions of Skyrmions with domain walls

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