Noncommutative quantum field theory: unitarity and discrete time

The unitarity condition for noncommutative field theories on compact space- times is considered. Although such theories are free of ultraviolet diverge nces, the compactness of space-like coordinates implies discreteness of the time variable which leads to appearance of unphysical modes and violation of unitarity even in absence of the star-product in the interaction terms. Thus, this conclusion holds also for other quantum field theories with disc rete time. We also discuss violation of causality in terms of commutators f or observables and possibility for a violation of the spin-statistics theor em. (C) 2001 Elsevier Science B.V. All rights reserved.