Paolo Aschieri et al 2005 Class. Quantum Grav. 22 3511 doi:10.1088/0264-9381/22/17/011
A gravity theory on noncommutative spaces
Paolo Aschieri1, Christian Blohmann2,3, Marija Dimitrijević4,5,6, Frank Meyer4,5, Peter Schupp2 and Julius Wess4,5
Show affiliationsA deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter θ. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different from the undeformed one. Based on this deformed algebra, a covariant tensor calculus is constructed and all the concepts such as metric, covariant derivatives, curvature and torsion can be defined on the deformed space as well. The construction of these geometric quantities is presented in detail. This leads to an action invariant under the deformed diffeomorphism algebra and can be interpreted as a θ-deformed Einstein–Hilbert action. The metric or the vierbein field will be the dynamical variable as they are in the undeformed theory. The action and all relevant quantities are expanded up to second order in θ.
- PACS
- MSC
- Subjects
- Dates
-
Issue 17 (7 September 2005)
Received 12 May 2005
Published 10 August 2005
-
A gravity theory on noncommutative spaces
Paolo Aschieri et al 2005 Class. Quantum Grav. 22 3511
-
Anomalous magnetoresistance of magnetic multilayers
R Seviour et al 2000 J. Phys.: Condens. Matter 12 L621
-
Low frequency noise in Co/Al2O3
δ(Fe)
/Ni80Fe20 magnetic tunnel junctions
R Guerrero et al 2002 J. Phys. D: Appl. Phys. 35 1761
-
C II* Absorption in Damped Lyα Systems. I. Star Formation Rates in a Two-Phase Medium
Arthur M. Wolfe et al. 2003 ApJ 593 215
-
Transport in single-molecule transistors: Kondo physics and negative differential resistance
Lam H Yu and Douglas Natelson 2004 Nanotechnology 15 S517
-
Incorporating a vascular term into a reference region model for the analysis of DCE-MRI data: a simulation study
A Z Faranesh and T E Yankeelov 2008 Phys. Med. Biol. 53 2617
-
Cleaved-edge overgrowth of aligned InAs islands on GaAs(110)
C X Cui et al 2005 Nanotechnology 16 2661
-
Chandra Observations of the "Dark" Moon and Geocoronal Solar Wind Charge Transfer
B. J. Wargelin et al. 2004 ApJ 607 596
-
Observation of Shubnikov–de Haas oscillations in the quasi-one-dimensional Bechgaard salt (TMTSF)2FSO3
O H Chung et al 2003 J. Phys.: Condens. Matter 15 7297
-
Magnetic domains in Ni–Mn–Ga martensitic thin films
V A Chernenko et al 2005 J. Phys.: Condens. Matter 17 5215