Four-Dimensional Twisted Group Lattices

TL;DR

This paper explores four-dimensional twisted group lattices as models for space-time, demonstrating their physical interpretability and suitability for field theories, including solutions for free and non-abelian gauge theories.

Contribution

It introduces four-dimensional twisted group lattices with physical interpretation and develops methods to formulate and solve field theories on these structures.

Findings

All irreducible representations for free field theory are identified.

Non-abelian gauge theory on 2D twisted group lattice is solved.

Discrete symmetries replace continuous space-time symmetries.

Abstract

Four-dimensional twisted group lattices are used as models for space-time structure. Compared to other attempts at space-time deformation, they have two main advantages: They have a physical interpretation and there is no difficulty in putting field theories on these structures. We present and discuss ordinary and gauge theories on twisted group lattices. We solve the free field theory case by finding all the irreducible representations. The non-abelian gauge theory on the two-dimensional twisted group lattice is also solved. On twisted group lattices, continuous space-time translational and rotational symmetries are replaced by discrete counterparts. We discuss these symmetries in detail. Four-dimensional twisted group lattices can also be used as models for non-trivial discrete compactifactions of certain ten-dimensional spaces.