It is extended to twisted spectral triples the fluctuations of the metric as bounded perturbations of the Dirac operator that arises when a spectral triple is exported between Morita equivalent algebras, as well as gauge transformations which are obtained by the action of the unitary endomorphisms of the module implementing the Morita equivalence. It is firstly shown that the twisted-gauged Dirac operators, previously introduced to generate an extra scalar field in the spectral description of the standard model of elementary particles, in fact follow from Morita equivalence between twisted spectral triples. The law of transformation of the gauge potentials turns out to be twisted in a natural way. In contrast with the non-twisted case, twisted fluctuations do not necessarily preserve the self-adjointness of the Dirac operator. For a self-Morita equivalence, conditions are obtained in order to maintain self-adjointness that are solved explicitly for the minimal twist of a Riemannian manifold.

Gauge transformations for twisted spectral triples

Landi, Giovanni
;
Martinetti, Pierre
2018-01-01

Abstract

It is extended to twisted spectral triples the fluctuations of the metric as bounded perturbations of the Dirac operator that arises when a spectral triple is exported between Morita equivalent algebras, as well as gauge transformations which are obtained by the action of the unitary endomorphisms of the module implementing the Morita equivalence. It is firstly shown that the twisted-gauged Dirac operators, previously introduced to generate an extra scalar field in the spectral description of the standard model of elementary particles, in fact follow from Morita equivalence between twisted spectral triples. The law of transformation of the gauge potentials turns out to be twisted in a natural way. In contrast with the non-twisted case, twisted fluctuations do not necessarily preserve the self-adjointness of the Dirac operator. For a self-Morita equivalence, conditions are obtained in order to maintain self-adjointness that are solved explicitly for the minimal twist of a Riemannian manifold.
2018
Pubblicato
https://link.springer.com/article/10.1007%2Fs11005-018-1099-3
File in questo prodotto:
File Dimensione Formato  
s11005-018-1099-3.pdf

Accesso chiuso

Tipologia: Documento in Versione Editoriale
Licenza: Copyright Editore
Dimensione 665.79 kB
Formato Adobe PDF
665.79 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
2925619_s11005-018-1099-3-PostPrint.pdf

accesso aperto

Descrizione: Post Print VQR3
Tipologia: Bozza finale post-referaggio (post-print)
Licenza: Digital Rights Management non definito
Dimensione 970.32 kB
Formato Adobe PDF
970.32 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2925619
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 12
social impact