Real Part of Twisted-by-Grading Spectral Triples

Abstract

After a brief review of the applications of twisted spectral triples to physics, we adapt to the twisted case the notion of the real part of a spectral triple. In particular, when one twists a usual spectral triple by its grading, we show that - depending on the 𝛫𝛰 dimension - the real part is either twisted as well, or is the intersection of the initial algebra with its opposite. We illustrate this result with the spectral triple of the standard model.