Letters in Mathematical Physics

, Volume 108, Issue 5, pp 1323–1340 | Cite as

The Standard Model in noncommutative geometry: fundamental fermions as internal forms

  • Ludwik Dąbrowski
  • Francesco D’Andrea
  • Andrzej Sitarz


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.


Spectral triples Morita equivalence Standard Model 

Mathematics Subject Classification

Primary 58B34 Secondary 46L87 81T13 



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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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Scuola Internazionale Superiore di Studi Avanzati (SISSA)TriesteItaly
  2. 2.Università di Napoli “Federico II”NaplesItaly
  3. 3.I.N.F.N. Sezione di NapoliNaplesItaly
  4. 4.Instytut Fizyki Uniwersytetu JagiellońskiegoKrakówPoland
  5. 5.IMPANWarszawaPoland

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