A gravity theory on noncommutative spaces
作者： Paolo Aschieri , Christian Blohmann , Marija Dimitrijević , Frank Meyer , Peter Schupp
DOI: 10.1088/0264-9381/22/17/011
关键词: Noncommutative geometry 、 Covariant transformation 、 Mathematical physics 、 Tensor calculus 、 Physics 、 Quantum mechanics 、 Cartan formalism 、 Einstein–Hilbert action 、 Leibniz integral rule 、 Covariant derivative 、 Covariance and contravariance of vectors
摘要: A deformation of the algebra diffeomorphisms is constructed for canonically deformed spaces with constant parameter ?. The algebraic relations remain same, whereas comultiplication rule (Leibniz rule) different from undeformed one. Based on this algebra, a covariant tensor calculus and all concepts such as metric, derivatives, curvature torsion can be defined space well. construction these geometric quantities presented in detail. This leads to an action invariant under diffeomorphism interpreted ?-deformed Einstein?Hilbert action. metric or vierbein field will dynamical variable they are theory. relevant expanded up second order
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