# Abelian Higgs model with charge conjugate boundary conditions

## TL;DR

This paper investigates the abelian Higgs model on the lattice with charge conjugate boundary conditions, constructing gauge-invariant operators to analyze particle masses and phase transitions.

## Contribution

It introduces a gauge-invariant scalar operator for the charged field and compares mass calculations across different phases, providing new insights into the model's spectrum.

## Key findings

- Charged scalar mass matches Coulomb gauge calculations in Coulomb phase
- Gauge-invariant operator effectively measures Higgs boson mass
- Charged particles vanish from the spectrum in the confined regime

## Abstract

The abelian Higgs model is studied on the lattice with charge conjugate boundary conditions. A locally gauge invariant operator for the charged scalar field is constructed and the charged scalar particle mass is calculated in the Coulomb phase of the lattice model. Agreement is found with the mass calculated in Coulomb gauge. The gauge invariant scalar field operator is used to calculate the Higgs boson mass in the Higgs region and to show that the charged particle disappears from the spectrum in the confined regime.