The Lagrangian Loop Representation of Lattice U(1) Gauge Theory

TL;DR

This paper develops a Lagrangian formalism for the Hamiltonian lattice loop representation of U(1) gauge theory, connecting loop operators to string-like actions and demonstrating their use in Monte Carlo simulations.

Contribution

It introduces a Lagrangian formalism for the lattice loop representation of U(1) gauge theory, linking loop operators to string actions and enabling Monte Carlo studies.

Findings

Loop classical action proportional to loop world sheet area

Connection between loop operators and Nambu string action

Monte Carlo simulation of the loop action

Abstract

It is showed how the Hamiltonian lattice $loop$ $representation$ can be cast straightforwardly in the Lagrangian formalism. The procedure is general and here we present the simplest case: pure compact QED. This connection has been shaded by the non canonical character of the algebra of the fundamental loop operators. The loops represent tubes of electric flux and can be considered the dual objects to the Nielsen-Olesen strings supported by the Higgs broken phase. The lattice loop classical action corresponding to the Villain form is proportional to the quadratic area of the loop world sheets and thus it is similar to the Nambu string action. This loop action is used in a Monte Carlo simulation and its appealing features are discussed.