A simplicial gauge theory

TL;DR

This paper introduces a discretized gauge theory framework on simplicial meshes, ensuring gauge invariance and consistency, along with a discrete version of Noether's theorem, bridging finite element methods and gauge theories.

Contribution

It presents a novel discretized gauge theory action on simplicial meshes that maintains gauge invariance and includes a proof of consistency and a discrete Noether's theorem.

Findings

The proposed action is discretely gauge invariant.

The method is consistent with continuous gauge theories.

A discrete Noether's theorem is established for the framework.

Abstract

We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consistency. A discrete Noether's theorem that can be applied to our setting, is also proved.