Matter Fields in the Lagrangian Loop Representation: Scalar QED

TL;DR

This paper extends the Lagrangian loop gauge invariant representation to include matter fields, specifically in the lattice compact U(1)-Higgs model, and explores its phase diagram through numerical simulations.

Contribution

It introduces a method to incorporate matter fields into the Lagrangian loop representation and maps the phase diagram of the U(1)-Higgs model.

Findings

Partition function expressed as sum over surfaces

Numerical simulation of loop action performed

Mapped out the beta-gamma phase diagram

Abstract

We present the extension of the Lagrangian loop gauge invariant representation in such a way to include matter fields. The partition function of lattice compact U(1)-Higgs model is expressed as a sum over closed as much as open surfaces. We have simulated numerically the loop action equivalent to the Villain form of the action and mapped out the beta-gamma phase diagram of this model.