M. Chaichian et al., Quantum field theory on noncommutative space-time: The relation between ultraviolet behaviour, topology and symmetry, MOD PHY L A, 16(4-6), 2001, pp. 235-240
We study properties of a scalar quantum field theory on two-dimensional non
commutative spacetimes. We show that ultraviolet behaviour of a field theor
y on noncommutative spaces is sensitive to the topology of the space time,
namely to its compactness. The compactness of space-like coordinates implie
s discreteness of the time variable which leads to appearance of unphysical
modes and violation of unitarity even in the absence of a star-product in
the interaction terms. Thus, this conclusion holds also for other quantum f
ield theories with discrete time.