Abstract
Given the algebra, Hilbert space H, grading and real structure of the finite spectral triple of the Standard Model, we classify all possible Dirac operators such that H is a self-Morita equivalence bimodule for the associated Clifford algebra.
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28 August 2019
The original version of the acknowledgement unfortunately contained a mistake.
28 August 2019
The original version of the acknowledgement unfortunately contained a mistake.
Notes
For a general spectral triple, despite the notations, this is not the same decomposition that appears in [7, §4], although in the Standard Model case the two decompositions coincide.
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Acknowledgements
L.D. is grateful for his support at IMPAN provided by Simons-Foundation Grant 346300 and a Polish Government MNiSW 2015–2019 matching fund. A.S. acknowledges the support from the Grant NCN 2015/19/B/ST1/03098. This work is part of the project Quantum Dynamics sponsored by the EU-grant RISE 691246 and Polish Government grant 317281.
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Dąbrowski, L., D’Andrea, F. & Sitarz, A. The Standard Model in noncommutative geometry: fundamental fermions as internal forms. Lett Math Phys 108, 1323–1340 (2018). https://doi.org/10.1007/s11005-017-1036-x
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DOI: https://doi.org/10.1007/s11005-017-1036-x