Abstract
This paper summarizes and gives new extensions of previous work of the author and collaborative work of the author with Pierre Noyes. In the present paper we give a new generalization of the Feynman-Dyson derivation of electromagnetism in a non-commutative context. In this form, the theory extends to gauge fields and is entirely a consequence of a choice of the definition of derivatives as commutators and the choice of relationship between temporal and spatial derivatives. The paper uses diagrammatic techniques and discusses these issues in the context of discrete physical models.
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