Mass gap in weakly coupled Abelian Higgs on a unit lattice

Abstract

We study the problem of mass generation in particle physics. In the Standard Model, the interaction of a particle with the Higgs boson is responsible for its mass generation, known as the Higgs mechanism. Our model is a weakly coupled Abelian Higgs theory on a unit lattice in space-time dimensions d greater than equal to 2. We give a rigorous, non - perturbative proof of the Higgs mechanism by establishing a mass gap in this model. We apply a new power series cluster expansion and show the existence of a mass gap for the observable electromagnetic field-strength tensor. Our method provides a simple and clean alternative to the decoupling clusterexpansions.