Momentum and Hamiltonian in Complex Action Theory

Details Momentum and Hamiltonian in Complex Action Theory Momentum and Hamiltonian in Complex Action Theory

2011-05-06

arxiv.org/abs/1105.1294v3

Physics

Quantum Physics

Latex 29 pages, 2 figures, title changed, references added, presentation improved, typo corrected

Scientific paper

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 $\xi$-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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