Inequivalence of the Massive Vector Meson and Higgs Models on a Manifold with Boundary

TL;DR

This paper demonstrates that the massive vector meson and Higgs models, though seemingly equivalent, are only truly equivalent under specific boundary conditions when defined on manifolds with boundaries, highlighting boundary effects in gauge theories.

Contribution

It provides a detailed analysis showing the inequivalence of these models on manifolds with boundaries, clarifying the role of boundary conditions in gauge theory equivalences.

Findings

Models are only equivalent for specific boundary conditions.

Boundary effects break naive gauge-fixing equivalence.

Explicit quantization on manifolds with boundary reveals differences.

Abstract

The exact quantization of two models, the massive vector meson model and the Higgs model in the London limit, both describing massive photons, is presented. Even though naive arguments (based on gauge-fixing) may indicate the equivalence of these models, it is shown here that this is not true in general when we consider these theories on manifolds with boundaries. We show, in particular, that they are equivalent only for a special choice of the boundary conditions that we are allowed to impose on the fields.