Gauge-invariance in cellular automata
Formal Languages and Automata Theory
2022-01-25 v2 Cellular Automata and Lattice Gases
Quantum Physics
Abstract
Gauge-invariance is a fundamental concept in Physics -- known to provide mathematical justification for the fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts directly in terms of Cellular Automata. More precisely, the notions of gauge-invariance and gauge-equivalence in Cellular Automata are formalized. A step-by-step gauging procedure to enforce this symmetry upon a given Cellular Automaton is developed, and three examples of gauge-invariant Cellular Automata are examined.
Keywords
Cite
@article{arxiv.2004.03656,
title = {Gauge-invariance in cellular automata},
author = {Pablo Arrighi and Giuseppe Di Molfetta and Nathanaël Eon},
journal= {arXiv preprint arXiv:2004.03656},
year = {2022}
}
Comments
This article supersedes arXiv:1802.07644 and arXiv:1908.01229