Momentum and hamiltonian in complex action theory

Keiichi Nagao; Holger Frits Bech Nielsen

doi:10.1142/S0217751X12500765

Momentum and hamiltonian in complex action theory

Keiichi Nagao, Holger Frits Bech Nielsen

Theoretical high energy, astroparticle and gravitational physics

9 Citations (Scopus)

Abstract

In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q.

Original language	English
Journal	International Journal of Modern Physics A
Volume	27
Issue number	14
Pages (from-to)	1250076
Number of pages	30
ISSN	0217-751X
DOIs	https://doi.org/10.1142/S0217751X12500765
Publication status	Published - 10 Jun 2012

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Faculty of Science

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title = "Momentum and hamiltonian in complex action theory",

abstract = "In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q.",

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TY - JOUR

T1 - Momentum and hamiltonian in complex action theory

AU - Nagao, Keiichi

AU - Nielsen, Holger Frits Bech

PY - 2012/6/10

Y1 - 2012/6/10

N2 - In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q.

AB - In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q.

KW - Faculty of Science

KW - Backward causation, quantum physics, nonhermitean Hamiltonian

U2 - 10.1142/S0217751X12500765

DO - 10.1142/S0217751X12500765

M3 - Journal article

SN - 0217-751X

VL - 27

SP - 1250076

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

IS - 14

ER -

Momentum and hamiltonian in complex action theory

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