Field theory amplitudes in a space with SU(2) fuzziness

Abstract

The structure of transition amplitudes in field theory in a three-dimensional space whose spatial coordinates are noncommutative and satisfy the SU(2) Lie algebra commutation relations is examined. In particular, the basic notions for constructing the observables of the theory as well as subtleties related to the proper treatment of $\delta$ distributions (corresponding to conservation laws) are introduced. Explicit examples are given for scalar field theory amplitudes in the lowest order of perturbation.

arXiv comment20 pages, no figs, LaTeX, to appear in EPJ-C

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Cited by in corpus (11)

• Loop diagrams in space with SU(2) fuzziness
• 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
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories
• Eigenvalue problem for radial potentials in space with SU(2) fuzziness