Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
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.