Classical Aspects of the Abelian Higgs Model on the Light Front

TL;DR

This paper explores how the canonical structure of the Abelian Higgs model on the light front varies with boundary conditions, revealing different zero-mode behaviors and implications for scalar field vevs.

Contribution

It uncovers a novel boundary-dependent change in the canonical structure and zero-mode constraints of the Abelian Higgs model within DLCQ framework.

Findings

Zero-mode constraints depend on boundary conditions.

Scalar field vev can be realized through background field minimization.

Different boundary conditions lead to distinct zero-mode dynamics.

Abstract

We investigate canonical structure of the Abelian Higgs model within the framework of DLCQ. Careful boundary analysis of differential equations, such as the Euler-Lagrange equations, leads us to a novel situation where the canonical structure changes in a drastic manner depending on whether the (light-front) spatial Wilson line is periodic or not. In the former case, the gauge-field ZM takes discrete values and we obtain the so-called ``Zero-Mode Constraints'' (ZMCs), whose semiclassical solutions give a nonzero vev to the scalar fields. Contrary, in the latter case, we have no ZMC and the scalar ZMs remain dynamical as well as the gauge-field ZM. In order to give classically nonzero vev to the scalar field, we work in a background field which minimizes the light-front energy.