Exotic Structure in theσModel

Abstract

In the Gell-Mann-Levy $\sigma$ model, although the soliton by itself is unstable to collapse, the author finds a stable self-consistent solution of a valence (single-particle) nucleon bound state in a soliton (hedgehog) configuration of the meson fields. This solution has baryon number 2 and in the neglect of quantum fluctuations its energy is found to be less than $m_N=g〈\sigma 〉 (=g{f}_{\pi })$, the mass of the usual plane-wave nucleon.