We study perturbations of the flat geometry of the noncommutative two-dimensional torus T2θ (with irrational θ). They are described by spectral triples (Aθ,H,D) , with the Dirac operator D, which is a differential operator with coefficients in the commutant of the (smooth) algebra A θ of Tθ . We show, up to the second order in perturbation, that the ζ-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We also calculate first two terms of the perturbative expansion of the corresponding local scalar curvature.

Curved noncommutative torus and Gauss--Bonnet

Dabrowski, Ludwik;
2013-01-01

Abstract

We study perturbations of the flat geometry of the noncommutative two-dimensional torus T2θ (with irrational θ). They are described by spectral triples (Aθ,H,D) , with the Dirac operator D, which is a differential operator with coefficients in the commutant of the (smooth) algebra A θ of Tθ . We show, up to the second order in perturbation, that the ζ-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We also calculate first two terms of the perturbative expansion of the corresponding local scalar curvature.
2013
54
1
013518
Dabrowski, Ludwik; Sitarz, A.
File in questo prodotto:
File Dimensione Formato  
JMP54.pdf

non disponibili

Licenza: Non specificato
Dimensione 458.48 kB
Formato Adobe PDF
458.48 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/20.500.11767/11448
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 31
  • ???jsp.display-item.citation.isi??? 30
social impact