First Simulation Results for the Photon in a Non-Commutative Space

TL;DR

This paper reports preliminary simulation results of quantum electrodynamics in a non-commutative four-dimensional space-time using a fuzzy lattice and matrix model, aiming to explore potential observable effects of space-time non-commutativity.

Contribution

First simulation results for QED in non-commutative space-time using a fuzzy lattice and matrix model, providing a basis for non-perturbative predictions of the photon.

Findings

Analysis of Wilson loops and Creutz ratios in the non-commutative setting

Feasibility of numerical simulation via matrix model mapping

Initial insights into non-perturbative photon properties

Abstract

We present preliminary simulation results for QED in a non-commutative 4d space-time, which is discretized to a fuzzy lattice. Its numerical treatment becomes feasible after its mapping onto a dimensionally reduced twisted Eguchi-Kawai matrix model. In this formulation we investigate the Wilson loops and in particular the Creutz ratios. This is an ongoing project which aims at non-perturbative predictions for the photon, which can be confronted with phenomenology in order to verify the possible existence of non-commutativity in nature.