Loop diagrams in space with SU(2) fuzziness

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 ${\varphi }^4$ 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.

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

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Cited by in corpus (12)

• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
• Quantum mechanics on space with SU(2) fuzziness
• Poisson structure on a space with linear SU(2) fuzziness
• Statistical mechanics of free particles on space with Lie type noncommutativity
• Closedness of orbits in a space with SU(2) Poisson structure
• Dirac theory on a space with linear Lie type fuzziness
• UV dimensional reduction to two from group valued momenta
• Gauge theory on a space with linear Lie type fuzziness
• Central force problem in space with SU(2) Poisson structure
• The similarity of attractive and repulsive forces on a lattice
• Eigenvalue problem for radial potentials in space with SU(2) fuzziness
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories