A gravity theory on non-commutative spaces

by Frank Meyer (CERN-PH/TH)

Tuesday 25 Oct 2005, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

I will start the seminar with introductory remarks about non-commutative spaces. Then a deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. Based on this deformed algebra a covariant tensor calculus is constructed and we introduce a non-commutative geometry: metric, covariant derivatives, curvature and torsion are defined on the deformed space. This leads to an action invariant under the deformed diffeomorphism algebra, a theta-deformed Einstein-Hilbert action. The metric or the vierbein field are the dynamical variable as they are in the undeformed theory. The action and all relevant quantities are expanded up to second order in theta. At the end I may comment on how to generalize this construction to a large class of non-commutative spaces.