Noncommutative geometry and gravity
Paolo AschieriDipartimento di Scienze e Tecnologie Avanzate, Universitá del Piemonte Orientale, and INFN, Via Bellini 25/G 15100 Alessandria, ItalyMarija DimitrijevićArnold Sommerfeld Center for Theoretical Physics, Fakultät für Physik, Universität München, Theresienstr. 37, 80333 München, GermanyFrank MeyerArnold Sommerfeld Center for Theoretical Physics, Fakultät für Physik, Universität München, Theresienstr. 37, 80333 München, GermanyJulius WessArnold Sommerfeld Center for Theoretical Physics, Fakultät für Physik, Universität München, Theresienstr. 37, 80333 München, Germany
2006en
ABI
Annotatsiya
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The class of noncommutative spaces studied is very rich. Non-anticommutative superspaces are also briefly considered. The differential geometry developed is covariant under deformed diffeomorphisms and it is coordinate independent. The main target of this work is the construction of Einstein's equations for gravity on noncommutative manifolds.
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