Simplicial gauge theory and quantum gauge theory simulation

TL;DR

This paper introduces a novel simplicial lattice gauge theory framework inspired by finite element methods, demonstrating convergence to continuum results and applying Monte Carlo simulations to quantum gauge fields.

Contribution

It presents a new formulation of simplicial gauge theory and applies it to quantum simulations, bridging finite element methods with lattice gauge theories.

Findings

Convergence towards continuum results demonstrated for SU(2) gauge fields.

Successful Monte Carlo simulations of quantum gauge fields performed.

Measurements of action and Wilson loops as functions of β obtained.

Abstract

We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed for several SU(2) gauge fields. Additionaly, we perform simplicial Monte Carlo quantum gauge field simulations involving measurements of the action as well as differently sized Wilson loops as functions of $\beta$.