  We analyze, starting from first principles, the quantization of field
theories, in order to find out to which problems a noncommutative time would
possibly lead. We examine the problem in the interaction picture
(Tomonaga-Schwinger equation), the Heisenberg picture
(Yang-Feldman-K\"all\'{e}n equation) and the path integral approach. They all
indicate inconsistency when time is taken as a noncommutative coordinate. The
causality issue appears as the key aspect, while the unitarity problem is
subsidiary. These results are consistent with string theory, which does not
admit a time-space noncommutative quantum field theory as its low-energy limit,
with the exception of light-like noncommutativity.
