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NCG

Seminar

Non-Commutative worlds

Kauffman, LH (Illinois at Chicago)
Wednesday 20 December 2006, 16:30-17:00

Seminar Room 1, Newton Institute

Abstract

This talk shows how forms of gauge theory, Hamiltonian mechanics, quantum mechanics and genreal relativity arise from a non-commutative framework for calculus and differential geometry. Discrete calculus is seen to fit into this pattern by a reformulation in terms of commutators. Differential geometry begins here, not with the concept of parallel translation, but with the concept of a physical trajectory and algebra related to the Jacobi identity that governs that trajectory. We discuss how Jacobi identity controls the Levi-Connection in this context. We generalize the Feynman-Dyson derivation of electormagnetism in a non-commutative context, and we show how natural constraints on non-commutative derivations give rise to fourth-order, generalizations of Einstein's equations for general relativity (joint work with Anthony Deakin and Clive Kilmister).

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