Loop Representation of the Partition Function of Lattice U(1) Gauge Theory

TL;DR

This paper introduces a loop (Lagrangian) representation for the partition function of pure compact lattice QED, linking loop world sheets with the classical lattice loop action proportional to their quadratic area.

Contribution

It presents a natural and straightforward loop representation for the partition function of lattice U(1) gauge theory, connecting it to topological string descriptions.

Findings

Loop representation proportional to quadratic area of loops.

Parallelism with topological Higgs phase in non-compact QED.

Provides a new perspective on lattice gauge theory formulations.

Abstract

We introduce in a natural and straigthforward way the $loop$ (Lagrangian) $representation$ for the partition function of pure compact lattice QED. The corresponding classical lattice loop action is proportional to the quadratic area of the loop world sheets. We discuss the parallelism between the $loop$ formulation of this model in terms of world sheets of loops and the $topological$ representation of the Higgs (broken) phase for the non-compact lattice QED in terms of world sheets of Nielsen-Olesen strings.