A gauge invariant reversible cellular automaton. (English) Zbl 1511.37020
Baetens, Jan M. (ed.) et al., Cellular automata and discrete complex systems. 24th IFIP WG 1.5 international workshop, AUTOMATA 2018, Ghent, Belgium, June 20–22, 2018. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10875, 1-12 (2018).
Summary: Gauge invariance is a fundamental concept in physics – known to provide mathematical justifications 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, we describe a step-by-step 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 of use in numerical analysis, quantum simulation, fault-tolerant (quantum) computation. From a mathematical perspective, discreteness provides a simple yet rigorous route straight to the core concepts.
For the entire collection see [Zbl 1390.68014].
For the entire collection see [Zbl 1390.68014].
MSC:
| 37B15 | Dynamical aspects of cellular automata |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
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