InterJournal Complex Systems, 49
Status: Accepted
Manuscript Number: [49]
Submission Date: 963011
Non-commutativity and discrete physics
Author(s): Louis Kauffman

Subject(s): CX.07

Category: Brief Article

Abstract:

The purpose of this paper is to present an introduction to work of the author and Pierre Noyes on discrete foundations of physicscite{KN1,KN2}. By taking a discrete stance from the very beginning, we find that the initial expressions of physical theory must occur in a context of non-commutative algebra and non-commutative vector analysis. In this way the formalism of quantum mechanics occurs first, but not necessarily with the usual interpretations. By following this line carefully we can show how the outlines of the well-known commutative forms of physical theory arise first in non-commutative form. This much, the present paper will make clear with specific examples and mathematical formulations. The exact relation of commutative and non-commutative theories raises a host of problems, and we shall use this paper to discuss these matters as well.

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