Mathematics

Motivated by the space of spinors on a Lorentzian manifold, I will defineKrein spectral triples, which generalise spectral triples from Hilbertspaces to Krein spaces. I will show that this Krein space approach allowsfor an improved formulation of the fermionic action for almost-commutativemanifolds, which is used to derive the Lagrangian fornoncommutative-geometric descriptions of particle physics models.This talk is based on arXiv:1505.01939.