Loop diagrams in space with SU(2) fuzziness
arXiv:0712.2216 · doi:10.1016/j.physletb.2008.02.002
Abstract
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 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 -function, rather than a three dimensional one, so that in transition rates only the planar corrections contribute.
v1: 12 pages, LaTeX, submitted PLB, v2: missing 2πis restored in 4-point function; last paragraph improved