Quantum Field Theory on Noncommutative Space-Times and the Persistence of Ultraviolet Divergences

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dc.creatorChaichian, M.
dc.creatorDemichev, A.
dc.creatorPresnajder, P.
dc.date1998-12-20
dc.date1999-04-13
dc.date.accessioned2026-07-07T04:25:45Z
dc.date.available2026-07-07T04:25:45Z
dc.descriptionWe study properties of a scalar quantum field theory on two-dimensional noncommutative space-times. Contrary to the common belief that noncommutativity of space-time would be a key to remove the ultraviolet divergences, we show that field theories on a noncommutative plane with the most natural Heisenberg-like commutation relations among coordinates or even on a noncommutative quantum plane with $E_q(2)$-symmetry have ultraviolet divergences, while the theory on a noncommutative cylinder is ultraviolet finite. Thus, ultraviolet behaviour of a field theory on noncommutative spaces is sensitive to the topology of the space-time, namely to its compactness. We present general arguments for the case of higher space-time dimensions and as well discuss the symmetry transformations of physical states on noncommutative space-times.
dc.description31 pages, Latex, minor typos corrected
dc.identifierhttps://arxiv.org/abs/hep-th/9812180
dc.identifierhttp://arxiv.org/abs/hep-th/9812180
dc.identifierNucl.Phys. B567 (2000) 360-390
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/55860
dc.subjectHigh Energy Physics - Theory
dc.titleQuantum Field Theory on Noncommutative Space-Times and the Persistence of Ultraviolet Divergences
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