Representations of classical groups on the lattice and its application to the field theory on discrete space-time

TL;DR

This paper investigates how classical group representations on lattices influence discrete space-time physics, deriving invariant transformations and applying them to field equations to adapt physical laws to discrete settings.

Contribution

It introduces integral transformations preserving lattice invariance and applies them to reformulate field equations in discrete space-time, bridging classical group theory and discrete physics.

Findings

Identified integral transformations invariant on lattice structures

Applied transformations to discretized field equations

Provided a mathematical framework for discrete space-time physics

Abstract

We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of any dimension invariant and apply these transformations to field equations.