Loop diagrams in space with SU(2) fuzziness

Understand

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 $\phi^4$ 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 $\delta$-function, rather than a three dimensional one, so that in transition rates only the planar corrections contribute.