Variational approach to bound states in scalar-gluon field theory

Abstract

Two variational approaches are employed to attack the bound-state problem of a charged scalar field interacting with an Abelian gauge field. The resulting variational equations allow for a qualitative discussion of all possible physical situations. Boundary conditions play a crucial role in their interpretation. A specially developed perturbation scheme yields hydrogenlike spectra. "Self-trapping" solutions and configurations with complete screening of the long-range force are discussed and are shown not to be obtainable by perturbation for small coupling. Metastable states appear for strong coupling.