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 $ϕ^4$ 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.
hep-th↗