Noncommutative field theory from angular twist

Abstract

We consider a noncommutative field theory in three space-time dimensions, with space-time star commutators reproducing a solvable Lie algebra. The -product can be derived from a twist operator and it is shown to be invariant under twisted Poincaré transformations. In momentum space the noncommutativity manifests itself as a noncommutative -deformed sum for the momenta, which allows for an equivalent definition of the -product in terms of twisted convolution of plane waves. As an application, we analyze the λφ4 field theory at one loop and discuss its UV/IR behavior. We also analyze the kinematics of particle decay for two different situations: the first one corresponds to a splitting of space-time where only space is deformed, whereas the second one entails a nontrivial -multiplication for the time variable, while one of the three spatial coordinates stays commutative.