Classical Loop Actions of Gauge Theories

TL;DR

This paper develops a general method to derive classical actions for gauge theories in the loop representation, demonstrating its application to electromagnetism and connecting it to lattice gauge theory for potential non-perturbative studies.

Contribution

It introduces a systematic procedure for determining classical loop actions of gauge theories, with explicit application to electromagnetism and lattice formulations.

Findings

Loop actions are equivalent to Wilson actions on the lattice.

The approach facilitates gauge-invariant Monte Carlo simulations.

Continuum actions serve as candidates for describing confining phases.

Abstract

Since the first attempts to quantize Gauge Theories and Gravity in the loop representation, the problem of the determination of the corresponding classical actions has been raised. Here we propose a general procedure to determine these actions and we explicitly apply it in the case of electromagnetism. Going to the lattice we show that the electromagnetic action in terms of loops is equivalent to the Wilson action, allowing to do Montecarlo calculations in a gauge invariant way. In the continuum these actions need to be regularized and they are the natural candidates to describe the theory in a ``confining phase''.