Real Part of Twisted-by-Grading Spectral Triples

Abstract

After a brief review on the applications of twisted spectral triples to physics, we adapt to the twisted case the notion of real part of a spectral triple. In particular, when one twists a usual spectral triple by its grading, we show that - depending on the $KO$ 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.

References in corpus (5)

• Why the Standard Model
• Resilience of the Spectral Standard Model
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
• Type III and spectral triples
• Minimal twist of almost commutative geometries