Field theory amplitudes in a space with SU(2) fuzziness

Abstract: The structure of transition amplitudes in field theory in a three-dimensional space whose spatial coordinates are noncommutative and satisfy the SU(2) Lie algebra commutation relations is examined. In particular, the basic notions for constructing the observables of the theory as well as subtleties related to the proper treatment of $\delta$ distributions (corresponding to conservation laws) are introduced. Explicit examples are given for scalar field theory amplitudes in the lowest order of perturbation.