Clifford Structures in Noncommutative Geometry and the Standard Model of Particle Physics

GAP Seminar

Meeting Details

For more information about this meeting, contact Ping Xu, Nigel Higson, Mathieu Stienon, Kendra Stauffer, Matthew Peddie.

Speaker: Francesco D'Andrea, University of Naples Federico II

Abstract: I will give a brief review of the spectral action approach to field theory, and discuss some recent results. On a Riemannian spin manifold M, an algebraic characterization of the module of Dirac spinors (sections of the spinor bundle) is as the Morita equivalence bimodule between the algebra of continuous functions on M and the Clifford algebra bundle. In the case of Hodge-Dirac operator on a oriented Riemannian manifold, on the other hand, the module of Hodge spinors can be characterized as self Morita equivalence bimodule for the Clifford algebra bundle. Both conditions admit a natural generalization to non-commutative manifolds and dictate some constraints on the form of the Dirac operator. I will report on a recent work with L. Dabrowski and A. Sitarz, where we investigate such constraints for the spectral triple of the Standard Model of elementary particles.

Room Reservation Information

Room Number: 320 Whitmore

Date: 09/19/2017

Time: 2:30pm - 3:20pm