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Entropy 2018, 20(7), 483; https://doi.org/10.3390/e20070483

Non-Commutative Worlds and Classical Constraints

1
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, USA
2
Department of Mechanics and Mathematics, Novosibirsk State University, Novosibirsk 630090, Russia
Received: 30 May 2018 / Revised: 18 June 2018 / Accepted: 19 June 2018 / Published: 21 June 2018
(This article belongs to the Special Issue Emergent Quantum Mechanics – David Bohm Centennial Perspectives)
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Abstract

This paper reviews results about discrete physics and non-commutative worlds and explores further the structure and consequences of constraints linking classical calculus and discrete calculus formulated via commutators. In particular, we review how the formalism of generalized non-commutative electromagnetism follows from a first order constraint and how, via the Kilmister equation, relationships with general relativity follow from a second order constraint. It is remarkable that a second order constraint, based on interlacing the commutative and non-commutative worlds, leads to an equivalent tensor equation at the pole of geodesic coordinates for general relativity. View Full-Text
Keywords: discrete calculus; iterant; commutator; diffusion constant; Levi-Civita connection; curvature tensor; constraints; Kilmister equation; Bianchi identity discrete calculus; iterant; commutator; diffusion constant; Levi-Civita connection; curvature tensor; constraints; Kilmister equation; Bianchi identity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kauffman, L.H. Non-Commutative Worlds and Classical Constraints. Entropy 2018, 20, 483.

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