  Studying the time development of the expectation value in the
future-not-included complex action theory, we point out that the momentum
relation (the relation analogous to $p=\frac{\partial L}{\partial \dot{q}}$),
which was derived via the Feynman path integral and was shown to be correct in
the future-included theory in our previous papers, is not valid in the
future-not-included theory. We provide the correct momentum relation in the
future-not-included theory, and argue that the future-not-included classical
theory is described by a certain real action. In addition, we provide another
way to understand the time development of the future-not-included theory by
utilizing the future-included theory. Furthermore, properly applying the method
used in our previous paper to the future-not-included theory by introducing a
formal Lagrangian, we derive the correct momentum relation in the
future-not-included theory.
