Krein spectral triples and the fermionic action

Authors

Koen van den Dungen, University of Wollongong, Australian National University, SISSA (Scuola Internazionale Superiore di Studi Avanzati)Follow

RIS ID

106237

Publication Details

van den Dungen, K. (2016). Krein spectral triples and the fermionic action. Mathematical Physics Analysis and Geometry, 19 (1), 4-1-4-22.

Abstract

Motivated by the space of spinors on a Lorentzian manifold, we define Krein spectral triples, which generalise spectral triples from Hilbert spaces to Krein spaces. This Krein space approach allows for an improved formulation of the fermionic action for almost-commutative manifolds. We show by explicit calculation that this action functional recovers the correct Lagrangians for the cases of electrodynamics, the electro-weak theory, and the Standard Model. The description of these examples does not require a real structure, unless one includes Majorana masses, in which case the internal spaces also exhibit a Krein space structure.