Lorentzian noncommutative geometry

01.12.2017, 09:30  –  Haus 9, Raum 2.22
Arbeitsgruppenseminar Analysis

Christian Brouder (Sorbonne Université, Paris)

Alain Connes' noncommutative geometry (NCG) is a powerful generalization of Riemannian geometry. Connes and collaborators showed that a Riemannian version of the standard model of particle physics could fit into the NCG framework.

Since the physical spacetime is Lorentzian and not Riemannian, a pseudo-Riemannian generalization of NCG has been a long-standing problem.

Such a generalization will be described in this talk. It is called indefinite noncommutative geometry (INCG) because the scalar product on a Hilbert space is replaced by an indefinite inner product (i.e. Hermitian form) on a Krein space. INCG are classified by two dimensions instead of one (the KO dimension). The INCG corresponding to the standard model in physical spacetime will be described.