ar X iv : h ep - t h / 05 12 13 4 v 1 1 3 D ec 2 00 5 A LORENTZ COVARIANT NONCOMMUTATIVE GEOMETRY

ar X iv : h ep - t h / 06 12 12 8 v 1 1 3 D ec 2 00 6 Riemannian Geometry of Noncommutative Surfaces

ar X iv : h ep - t h / 05 05 24 5 v 1 2 6 M ay 2 00 5 Commutator anomalies in noncommutative electrodynamics

We exploit the maps for fields and currents in a U(1) gauge theory relating the noncommutative and commutative (usual) descriptions to obtain the O(θ) structure of the commutator anomalies in noncommutative electrodynamics. These commutators involve the (covariant) current–current algebra and the (covariant) current–field algebra. We also establish the compatibility of the anomalous commutators...

ar X iv : h ep - t h / 05 01 01 7 v 1 4 J an 2 00 5 Lorentz invariance of scalar field action on κ - Minkowski space - time

We construct field theory on noncommutative κ-Minkowski spacetime. Having the Lorentz action on the noncommutative space-time coordinates we show that the field lagrangian is invariant. We show that noncommutativity requires replacing the Leibnitz rule with the coproduct one.

ar X iv : h ep - t h / 05 12 11 4 v 1 9 D ec 2 00 5 κ - Minkowski operators on Hilbert spaces April 12 , 2008

The algebra of functions on κ-Minkowski noncommutative spacetime is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction of integration in κ-Minkowski spacetime defined in terms of the usual trace of operators.

ar X iv : h ep - t h / 05 06 12 7 v 2 1 5 Ju n 20 05 Lorentz invariant supersymmetric mechanism for non ( anti ) commutative deformations of space - time geometry

A supersymmetric Lorentz invariant mechanism for superspace deformations is proposed. It is based on an extension of superspace by one λ a or several Majorana spinors associated with the Penrose twistor picture. Some examples of Lorentz invariant su-persymmetric Poisson and Mojal brackets are constructed and the correspondence: θ mn ↔ iψ m ψ n , C ab ↔ λ a λ b , Ψ a m ↔ ψ m λ a mapping the brac...