Loop diagrams in space with SU(2) fuzziness

Details Loop diagrams in space with SU(2) fuzziness Loop diagrams in space with SU(2) fuzziness

2007-12-13

arxiv.org/abs/0712.2216v2

Phys.Lett.B661:226-232,2008

Physics

High Energy Physics

High Energy Physics - Theory

v1: 12 pages, LaTeX, submitted PLB, v2: missing 2\pi is restored in 4-point function; last paragraph improved

Scientific paper

10.1016/j.physletb.2008.02.002

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.

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