Twisted Standard Model and its Krein structure -- in memoriam Manuele Filaci

Abstract

We review the contributions of Manuele Filaci - a PhD student from the university of Genova prematurely deceased a little more than a year ago - to the description of the Standard Model in noncommutative geometry. Building on Manuele's discovery that there exist various ways to minimally twist the spectral triple of the Standard Model, we study in a systematic way the inner product induced by the twist. Under loose assumptions, this product turns the Hilbert space of the spectral triple into a Krein space. For the Standard Model, the group of unitary with respect to the twisted product contains the symmetry group of twistors as a subgroup.

Proceedings of the conference "Applications of noncommutative geometry to gauge theories, field theories ans quantum spacetimes", CIRM (Marseille Luminy), aril 2025