A gauge-invariant reversible cellular automaton.

Gauge-invariance is a fundamental concept in physics---known to provide themathematical justification for all four fundamental forces. In this paper, weprovide discrete counterparts to the main gauge theoretical concepts, directlyin terms of Cellular Automata. More precisely, we describe a step-by-stepgauging procedure to enforce local symmetries upon a given Cellular Automaton.We apply it to a simple Reversible Cellular Automaton for concreteness. From aComputer Science perspective, discretized gauge theories may be applied tonumerical analysis, quantum simulation, fault-tolerant (quantum) computation.From a mathematical perspective, discreteness provides a simple yet rigorousroute straight to the core concepts.