On the momentum of gluons in Lattice Gauge Theory (LGT)

TL;DR

This paper discusses the gauge dependence issue in Fourier space preconditioning for Lattice Gauge Theory simulations and suggests that physical gluon momentum transfer can be used effectively with recent advances in generative models.

Contribution

It clarifies the gauge dependence problem and proposes that physical gluon momentum transfer can be utilized in LGT simulations with new generative modeling techniques.

Findings

Gauge dependence of momenta is a fake obstacle in LGT.

Gluon momentum transfer is a physical quantity.

Recent generative models enable practical simulations.

Abstract

Attempts to improve LGT simulation algorithms by Fourier space preconditioning have been handicapped by the gauge dependence of momenta, familiar from perturbation theory. The continuum theory has a gauge invariant energy-momentum density, indicating this to be a fake obstacle. While perturbation-theory momenta are evidently wrong for the task, momentum-transfer carried by gluons is physical. Simulations using these momenta may become practical in the near future thanks to recent progress in generative models, stochastic and/or deterministic.