Keiichi Nagao, Holger Bech Nielsen
Studying the time development of the expectation value in the future-not-included complex action theory we point out that the momentum relation (relation analogous to $p=\frac{\partial L}{\partial \dot{q}}$), which was derived via Feynman path integral and was shown to be right 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, applying the method used in our previous paper to the future-not-included theory properly by introducing a formal Lagrangian, we derive the correct momentum relation in the future-not-included theory.
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http://arxiv.org/abs/1304.4017
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