1998/12/31 by M. Chaichian, A. Demichev, P. Presnajder
Physics and Astronomy · #hep-th
published as Nucl.Phys. B567 (2000) 360-390 · 31 pages, Latex, minor typos corrected
arxiv created 1999/04/13 · arxiv updated 2009/11/30
We 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 Eq(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.