  General aspects of the quantization of field theories non-local in time are
discussed. The path integral on the basis of Schwinger's action principle and
the Bjorken-Johnson-Low prescription, which helps to recover the canonical
structure from the results of the path integral, are used as the main
machinery. A modified time ordering operation which formally restores unitarity
in field theories non-local in time is analyzed in detail. It is shown that the
perturbative unitarity and the positive energy condition, in the sense that
only the positive energy flows in the positive time direction for any fixed
time-slice in space-time, are not simultaneously satisfied for theories
non-local in time such as space-time noncommutative theory.
