The Gaussian approximation for interacting charged scalar fields

Abstract

The Gaussian effective-potential approach is used to explore the physics of charged \(\lambda(\phi^{+}\phi)^{2}\) theory in four space-time dimensions. We find and employ an appropriate trial system, parametrized by two effective masses, for obtaining an adequate Gaussian effective potential under conditions of the global U(1) symmetry and the finite temperature. A simple renormalization, accompanied by an explicit dimensional regularization, is employed. We find that the nontrivial approach arises from a bare coupling constant of a negative infinitesimal form, well known in the noncharged case as “precarious”. The behavior of this solution is discussed, and the symmetry breaking due to background charge density is discovered.