Non-Commutative Worlds and Classical Constraints

Louis H Kauffman

doi:10.3390/e20070483

Non-Commutative Worlds and Classical Constraints

Entropy (Basel). 2018 Jun 21;20(7):483. doi: 10.3390/e20070483.

Author

Louis H Kauffman^{1

2}

Affiliations

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.

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.

Keywords: Bianchi identity; Kilmister equation; Levi-Civita connection; commutator; constraints; curvature tensor; diffusion constant; discrete calculus; iterant.