Stable and unstable classical solutions in an effective gauge theory for low energy mesons

We study the stability of two related classical solutions in an effective gauge theory, which correctly describes the properties of π and rho mesons at low energies. The first solution (sphaleron) which excites only the rho field, with baryon number B=0 and energy Eapprox.=1.5 GeV, is unstable. The second (Skyrmion), which excites both the π and rho fields, with B=1 and Eapprox.=1.0 GeV, is perhaps stable locally. We show how to make this Skyrmion absolutely stable without raising its energy too much, both of which are desirable for identification with the nucleon. We comment on the potential of heavy ion collision experiments to study configuration space. The Skyrmion solution may also have some relevance for the electroweak interactions (now Eapprox.=10 TeV). (orig.)