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After a brief review on the applications of twisted spectral triples tophysics, we adapt to the twisted case the notion of real part of a spectraltriple. In particular, when one twists a usual spectral triple by its grading,we show that - depending on the $KO$ dimension - the real part is eithertwisted as well, or is the intersection of the initial algebra with itsopposite. We illustrate this result with the spectral triple of the standardmodel.

Real Part of Twisted-by-Grading Spectral Triples