1105.1294 (Keiichi Nagao et al.)

Momentum and Hamiltonian in Complex Action Theory    [PDF]

Keiichi Nagao, Holger Bech Nielsen

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 $q$.

View original: http://arxiv.org/abs/1105.1294