M. Chaichian et al., Quantum field theory on non-commutative space-times and the persistence ofultraviolet divergences, NUCL PHYS B, 567(1-2), 2000, pp. 360-390
We study properties of a scalar quantum field theory on two-dimensional non
-commutative space-times. Contrary to the common belief that non-commutativ
ity of space-time would be a key to remove the ultraviolet divergences, we
show that field theories on a non-commutative plane with the most natural H
eisenberg-like commutation relations among coordinates or even on a non-com
mutative quantum plane with E-q(2) symmetry have ultraviolet divergences, w
hile the theory on a non-commutative cylinder is ultraviolet finite. Thus,
ultraviolet behavior of a field theory on non-commutative spaces is sensiti
ve 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 non-commutative
space-times. (C) 2000 Elsevier Science B.V. Ail rights reserved.