A generalization of the Higgs model without dipole ghosts

Abstract

The Abelian Higgs model displays unorthodox features such as nonunitary translation operators and dipole singularities in the propagators of the Goldstone and the vector field. In order to circumvent mathematical difficulties due to these singularities, the Higgs model is here generalized by the inclusion of a mass term in the free Lagrangian of the vector field. This model is first systematically discussed on the classical level, including the construction of a positive-definite energy density and the formulation of the classical counterpart to spontaneous symmetry breaking. Then the Fock-space representation is given for the linearized model, which is shown to possess unitary translation operators and to be free of dipole singularities. The propagator of the vector field is demonstrated to be well behaved in the ultraviolet limit. Four kinds of particles are shown to occur in the theory: vector, Goldstone, Higgs and gauge particles. The coupling between them is studied by simulation of the interaction through external sources. It turns out that the massive gauge particles always decouple from the other particles, which guarantees that they are unobservable. The coupling of the Goldstone particles is governed by the mass parameter of the vector field and vanishes only in the zero limit of this parameter.