Virial theorem and stability of localized solutions of relativistic classical interacting fields

The properties of classical meson fields interacting with the Dirac field are considered in more detail analytically. We obtain a virial relation between the kinetic and potential energy of the interacting Dirac field. The stability of the classical solutions of the coupled fields constrained to the lowest particle solution of the Dirac equation in three space dimensions is investigated. A criterion allowing the determination of stability of Abelian meson fields in interaction with the Dirac field is given.