We study perturbative noncommutative quantum gravity by expanding the gravitational field about a fixed classical background. A calculation of the one loop gravitational self-energy graph reveals that only the non-planar graviton loops are damped by oscillating internal momentum dependent factors. The noncommutative quantum gravity perturbation theory is not renormalizable beyond one loop for m...

We discuss various aspects of the noncommutative geometry a smooth subalgebra Toeplitz algebra. In particular, we study structure derivations on this subalgebra.

We give a general and nontechnical review of some aspects of non-commutative geometry as a tool to understand the structure of space-time. We discuss the motivations for the constructions of a noncom-mutative geometry, and the passage from commutative to noncommu-tative spaces. We then give a brief description of Connes approach to the standard model, of the noncommutative geometry of strings a...