Momentum relation and classical limit in the future-not-included complex action theory
Abstract
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 ), 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.
Keywords
Cite
@article{arxiv.1304.4017,
title = {Momentum relation and classical limit in the future-not-included complex action theory},
author = {Keiichi Nagao and Holger Bech Nielsen},
journal= {arXiv preprint arXiv:1304.4017},
year = {2019}
}
Comments
Latex 28 pages, 2 figures, typos corrected, the final version to appear in Prog.Theor.Exp.Phys. (v3) A missed $dt$-dependent normalization factor is properly considered in Section 3.1. The errors and typos mentioned in the erratum of PTEP are corrected. arXiv admin note: text overlap with arXiv:1205.3706