Matter on granular space-time

TL;DR

This paper extends the formalism of non-Abelian gauge theories on cell complex space-time, providing gauge-invariant actions and equations of motion that are independent of the cells' geometry, with illustrative examples for U(N) and SU(N).

Contribution

It introduces a generalized formalism for gauge fields on cell complex space-time that is independent of geometric assumptions, with explicit solutions for common gauge groups.

Findings

Gauge-invariant actions formulated without geometric cell references

Explicit solutions for U(N) and SU(N) gauge groups

Formalism applicable to non-Abelian gauge theories on discrete space-time

Abstract

We develop further the formalism of the non-Abelian gauge field theory on a cell complex space-time and show how the gauge-invariant action and the equations of motion for gauge fields interacting with spinors can be written without a reference to the geometrical nature of the cells of the cell complex. The general results are illustrated with examples of solutions of equations of motion for U(N) and SU(N) gauge groups.