2014•Unpublished venueRequires access

Noncommutative Geometry in Physics

Axel Marcillaud de Goursac

Abstract

Noncommutative geometry is a domain of Mathematics whose ideas have been inspired by quantum mechanics. We present briefly the philosophy of Noncommutative Geometry and its applications in different parts of mathematics: topology, measure theory, differential geometry, algebraic geometry and group theory. Finally, we see three examples of applications of Noncommutative geometry in Physics: the spectral version of the standard model of Chamseddine-Connes, a formulation of the integral quantum Hall effect due to Bellissard and Quantum Field theories on noncommutative space-time.

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Key concepts: Noncommutative geometry, Quantum differential calculus, Noncommutative quantum field theory, Noncommutative algebraic geometry, Spectral triple, Geometry, Differential geometry, Mathematics