Clifford Structures in Noncommutative Geometry and the Standard Model of Particle Physics
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
Time: 2:30pm - 3:20pm