Noncommutative Spaces and Gravity
Abstract
Description
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative spaces. Then the $θ$-deformation of diffeomorphisms is studied and a tensor calculus is defined. A deformed Einstein-Hilbert action invariant with respect to deformed diffeomorphisms is given. Finally, all noncommutative fields are expressed in terms of their commutative counterparts up to second order of the deformation parameter using the $\star$-product. This allows to study explicitly deviations to Einstein's gravity theory in orders of $θ$.
18 p., based on talks given at First Modave Summer School, June 2005, Modave (Belgium); HEP 2005, July 2005, Lisboa (Portugal); XXVIII Spanish Relativity Meeting, September 2005, Oviedo (Spain)
18 p., based on talks given at First Modave Summer School, June 2005, Modave (Belgium); HEP 2005, July 2005, Lisboa (Portugal); XXVIII Spanish Relativity Meeting, September 2005, Oviedo (Spain)