| Autor: |
Dąbrowski, Ludwik, D'Andrea, Francesco, Magee, Adam M. |
| Zdroj: |
Mathematical Physics, Analysis & Geometry; Jun2021, Vol. 24 Issue 2, p1-27, 27p |
| Abstrakt: |
An interesting feature of the finite-dimensional real spectral triple (A,H,D,J) of the Standard Model is that it satisfies a "second-order" condition: conjugation by J maps the Clifford algebra C ℓ D (A) into its commutant, which in fact is isomorphic to the Clifford algebra itself (H is a self-Morita equivalence C ℓ D (A) -bimodule). This resembles a property of the canonical spectral triple of a closed oriented Riemannian manifold: there is a dense subspace of H which is a self-Morita equivalence C ℓ D (A) -bimodule. In this paper we argue that on manifolds, in order for the self-Morita equivalence to be implemented by a reality operator J, one has to introduce a "twist" and weaken one of the axioms of real spectral triples. We then investigate how the above mentioned conditions behave under products of spectral triples. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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