Higgs mechanism in a light front formulation

TL;DR

This paper presents a straightforward derivation of the Higgs mechanism within an abelian light front field theory, emphasizing a finite volume approach and avoiding gauge fixing.

Contribution

It introduces a novel light front formulation of the Higgs mechanism using finite volume quantization and constructs degenerate vacua as coherent states.

Findings

Massive vector field generated without gauge fixing

Effective Hamiltonian describes a massive gauge boson

Degenerate vacua as coherent states minimize light front energy

Abstract

We give a simple derivation of the Higgs mechanism in an abelian light front field theory. It is based on a finite volume quantization with antiperiodic scalar fields and a periodic gauge field. An infinite set of degenerate vacua in the form of coherent states of the scalar field that minimize the light front energy, is constructed. The corresponding effective Hamiltonian descibes a massive vector field whose third component is generated by the would-be Goldstone boson. This mechanism, understood here quantum mechanically in the form analogous to the space-like quantization, is derived without gauge fixing as well as in the unitary and the light cone gauge.