Field theories on spaces with linear fuzziness

Abstract

A noncommutative space is considered the position operators of which satisfy the commutativity relations of a Lie algebra. The basic tools for calculation on this space, including the product of the fields, inner product and the proper measure for integration are derived. Some general aspects of perturbative field theory calculations on this space are also discussed. Among the features of such models is that they are free from ultraviolet divergences (and hence free from UV/IR mixing as well), if the group is compact. The example of the group SO(3) or SU(2) is investigated in more detail.

12 pages, no figs., LaTeX. v2: Comments and discussions are added, e.g. on absence of UV/IR phenomena. No change in results

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• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
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• D-branes and the Noncommutative Torus
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Cited by in corpus (13)

• Field theory amplitudes in a space with SU(2) fuzziness
• Loop diagrams in space with SU(2) fuzziness
• Poisson structure on a space with linear SU(2) fuzziness
• Quantum mechanics on space with 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
• TeV-photon paradox and space with SU(2) fuzziness
• Dirac theory on a space with linear Lie type fuzziness
• 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