Theory including future not excluded: Formulation of complex action theory II

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Theory including future not excluded : Formulation of complex action theory II. / Nagao, K.; Nielsen, H.B.

In: Progress of Theoretical and Experimental Physics, Vol. 2013, No. 2, 04.02.2013, p. 023B04.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Nagao, K & Nielsen, HB 2013, 'Theory including future not excluded: Formulation of complex action theory II', Progress of Theoretical and Experimental Physics, vol. 2013, no. 2, pp. 023B04. https://doi.org/10.1093/ptep/pts084

APA

Nagao, K., & Nielsen, H. B. (2013). Theory including future not excluded: Formulation of complex action theory II. Progress of Theoretical and Experimental Physics, 2013(2), 023B04. https://doi.org/10.1093/ptep/pts084

Vancouver

Nagao K, Nielsen HB. Theory including future not excluded: Formulation of complex action theory II. Progress of Theoretical and Experimental Physics. 2013 Feb 4;2013(2):023B04. https://doi.org/10.1093/ptep/pts084

Author

Nagao, K. ; Nielsen, H.B. / Theory including future not excluded : Formulation of complex action theory II. In: Progress of Theoretical and Experimental Physics. 2013 ; Vol. 2013, No. 2. pp. 023B04.

Bibtex

@article{fd9576f160fe40449926b6638fee18b5,
title = "Theory including future not excluded: Formulation of complex action theory II",
abstract = "We study a complex action theory (CAT) whose path runs over not only past but also future. We show that, if we regard a matrix element defined in terms of the future state at time T and the past state at time TA as an expectation value in the CAT, then we are allowed to have the Heisenberg equation, Ehrenfest's theorem, and the conserved probability current density. In addition,we showthat the expectation value at the present time t of a future-included theory for large T - t and large t - T corresponds to that of a future-not-included theory with a proper inner product for large t - T. Hence, the CAT with future explicitly present in the formalism and influencing in principle the past is not excluded phenomenologically, because the effects are argued to be very small in the present era. Furthermore, we explicitly derive the Hamiltonian for the future state via a path integral, and confirm that it is given by the Hermitian conjugate of the Hamiltonian for the past state.",
author = "K. Nagao and H.B. Nielsen",
year = "2013",
month = feb,
day = "4",
doi = "10.1093/ptep/pts084",
language = "English",
volume = "2013",
pages = "023B04",
journal = "Progress of Theoretical Physics Supplement",
issn = "2050-3911",
publisher = "Oxford University Press",
number = "2",

}

RIS

TY - JOUR

T1 - Theory including future not excluded

T2 - Formulation of complex action theory II

AU - Nagao, K.

AU - Nielsen, H.B.

PY - 2013/2/4

Y1 - 2013/2/4

N2 - We study a complex action theory (CAT) whose path runs over not only past but also future. We show that, if we regard a matrix element defined in terms of the future state at time T and the past state at time TA as an expectation value in the CAT, then we are allowed to have the Heisenberg equation, Ehrenfest's theorem, and the conserved probability current density. In addition,we showthat the expectation value at the present time t of a future-included theory for large T - t and large t - T corresponds to that of a future-not-included theory with a proper inner product for large t - T. Hence, the CAT with future explicitly present in the formalism and influencing in principle the past is not excluded phenomenologically, because the effects are argued to be very small in the present era. Furthermore, we explicitly derive the Hamiltonian for the future state via a path integral, and confirm that it is given by the Hermitian conjugate of the Hamiltonian for the past state.

AB - We study a complex action theory (CAT) whose path runs over not only past but also future. We show that, if we regard a matrix element defined in terms of the future state at time T and the past state at time TA as an expectation value in the CAT, then we are allowed to have the Heisenberg equation, Ehrenfest's theorem, and the conserved probability current density. In addition,we showthat the expectation value at the present time t of a future-included theory for large T - t and large t - T corresponds to that of a future-not-included theory with a proper inner product for large t - T. Hence, the CAT with future explicitly present in the formalism and influencing in principle the past is not excluded phenomenologically, because the effects are argued to be very small in the present era. Furthermore, we explicitly derive the Hamiltonian for the future state via a path integral, and confirm that it is given by the Hermitian conjugate of the Hamiltonian for the past state.

UR - http://www.scopus.com/inward/record.url?scp=84876351632&partnerID=8YFLogxK

U2 - 10.1093/ptep/pts084

DO - 10.1093/ptep/pts084

M3 - Journal article

AN - SCOPUS:84876351632

VL - 2013

SP - 023B04

JO - Progress of Theoretical Physics Supplement

JF - Progress of Theoretical Physics Supplement

SN - 2050-3911

IS - 2

ER -

ID: 45576486