TY - JOUR
T1 - A gravity theory on noncommutative spaces
AU - Aschieri, Paolo
AU - Blohmann, Christian
AU - Dimitrijević, Marija
AU - Meyer, Frank
AU - Schupp, Peter
AU - Wess, Julius
PY - 2005/9/7
Y1 - 2005/9/7
N2 - A 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.
AB - A 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.
UR - http://www.scopus.com/inward/record.url?scp=24144475305&partnerID=8YFLogxK
U2 - 10.1088/0264-9381/22/17/011
DO - 10.1088/0264-9381/22/17/011
M3 - Article
SN - 0264-9381
VL - 22
SP - 3511
EP - 3532
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
IS - 17
ER -