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Non-Commutative Worlds and Classical Constraints.

Louis H Kauffman^1,2

¹Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, USA.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

This study explores constraints linking classical and discrete calculus, revealing connections between non-commutative electromagnetism and general relativity through commutator-based formalisms. These findings bridge discrete physics with established theories.

Keywords:

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

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Area of Science:

Theoretical Physics
Mathematical Physics

Background:

Existing research in discrete physics and non-commutative theories.
The need for a unified framework linking classical and discrete calculus.

Purpose of the Study:

To explore constraints linking classical and discrete calculus.
To investigate the consequences of these constraints on physical theories.
To establish connections between non-commutative electromagnetism and general relativity.

Main Methods:

Review of existing results in discrete physics and non-commutative worlds.
Formulation of constraints using commutators.
Analysis of first and second-order constraints.
Application of the Kilmister equation.

Main Results:

Generalized non-commutative electromagnetism derived from a first-order constraint.
Relationships with general relativity derived from a second-order constraint via the Kilmister equation.
A second-order constraint yields an equivalent tensor equation for general relativity.

Conclusions:

The study establishes a formal link between discrete calculus and established physics.
The findings suggest a deeper connection between non-commutative theories and general relativity.
The commutator-based approach offers a novel perspective on fundamental physics.