| We discuss noncommutative deformations of the geometry of space-time and of superspace. First, we consider gauge theories on noncommutative space-times. We develop two methods to construct explicitly Seiberg-Witten maps for any gauge group and to all orders in the deformation parameter, and we characterize the ambiguity inherent in their definition. Next, we deform the phase space of a superparticle to construct a supersymmetric extension of the Weyl-Moyal product, as a first step toward a supersymmetric version of Moyal string field theory. We find a noncommutative superspace isomorphic to the eleven-dimensional superPoincare algebra but with covariant constraints. We investigate the constraints and give an implicit definition of the noncommutative product. |
