Particle-like solutions in field theory

Abstract

A number of quantum field theories have the property that the field equations, studied as classical equations of motion, have particle-like solutions. These are spatially localized exact solutions, with a definite value of angular momentum. The role of these solutions in a fully quantum theory is the subject of investigation. We examine, in particular, the theory of a nonrelativistic scalar nucleon, coupled by a local interaction to a scalar meson field. The classical solution (whose spatial extent is a nucleon Bohr radius) is identified with a self-consistent field approximation to the one-nucleon state. However, quantum corrections to this approximation yield the same divergent self-energy as perturbation theory. In this example, the particle-like solutions have nothing to do with the ultraviolet divergences, but are relevant to the treatment of the finite part of the theory for strong coupling. The separation of the infinite part is trivial and is accomplished by a canonical transformation. The particle solutions still exist for the finite part for strong coupling.