Lorentz Covariant Lattice Gauge Theory

TL;DR

This paper introduces a novel Lorentz covariant lattice gauge theory technique that replaces the traditional lattice with a graph-based approach, preserving Lorentz symmetry and addressing a key limitation of standard lattice discretizations.

Contribution

It proposes a new method for lattice gauge theory that maintains exact Lorentz covariance using a graph-based metric, challenging the conventional discretization approach.

Findings

Eliminates Lorentz symmetry violation in lattice gauge theories

Demonstrates a graph-based metric approach for covariant simulations

Supports the possibility of a Lorentz covariant digital universe

Abstract

Lattice gauge theory's discretization of spacetime suffers from a drawback in that Lorentz covariance is lost because the axes of the lattice create preferred directions in spacetime. Smaller and smaller lattice spacings decrease the effect but fail to eliminate it completely. It has been argued recently that detecting such a set of preferred directions or similar constraints would indicate whether the universe itself has an underlying lattice, i.e. the digital universe hypothesis. In this paper, I demonstrate a technique for accomplishing lattice gauge theory simulations while maintaining exact Lorentz covariance by replacing the lattice with a lattice graph such that the metric is defined as a discrete, Lorentz covariant matrix potential over the graph rather than a metric over an underlying manifold. This technique eliminates the symmetry violation of standard lattice gauge theory and suggests that, even in a digital universe, Lorentz covariance can still hold.