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

M. Chaichian·A. Demichev·P. Presnajder
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Abstract

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 $E_q(2)$-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.

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M. Chaichian, A. Demichev, P. Presnajder. 1999-04-13. Quantum Field Theory on Noncommutative Space-Times and the Persistence of Ultraviolet Divergences. https://arxiv.org/abs/hep-th/9812180

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