Loop diagrams in space with SU(2) fuzziness

The structure of loop corrections is examined in a scalar field theory on a three-dimensional space whose spatial coordinates are noncommutative and satisfy SU(2) Lie algebra. In particular, the 2- and 4-point functions in ϕ4 scalar theory are calculated at the 1-loop order. The theory is UV-finite as the momentum space is compact. It is shown that the non-planar corrections are proportional to a one-dimensional δ-function, rather than a three-dimensional one, so that in transition rates only the planar corrections contribute.