A gaugeinvariant reversible cellular automaton
Abstract
Gaugeinvariance is a fundamental concept in physicsknown to provide the mathematical justification for all four fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts, directly in terms of Cellular Automata. More precisely, we describe a stepbystep gauging procedure to enforce local symmetries upon a given Cellular Automaton. We apply it to a simple Reversible Cellular Automaton for concreteness. From a Computer Science perspective, discretized gauge theories may be applied to numerical analysis, quantum simulation, faulttolerant (quantum) computation. From a mathematical perspective, discreteness provides a simple yet rigorous route straight to the core concepts.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.07644
 Bibcode:
 2018arXiv180207644A
 Keywords:

 Computer Science  Formal Languages and Automata Theory;
 Nonlinear Sciences  Cellular Automata and Lattice Gases;
 Quantum Physics
 EPrint:
 12 pages, 5 figures