Path Integrals for Pseudo-Hermitian Hamiltonians

Mekki Aouachria

Fabio Bagarello, Joshua Feinberg

Belal Ehsan Baaquie

The Euclidean action with acceleration has been analyzed in Ref. 1, and referred to henceforth as Paper I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation and destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.

Junqing Li, Yan-Gang Miao, Zhao Xue

Hugh F Jones, J. Mateo

Rima Rekik, Farida Halimi, Mekki Aouachria

The time development of a two-level system with a pseudo-Hermitian Hamiltonian is studied using the spin coherent state path integral. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions (θ,φ). Then it is determined exactly using perturbation methods. The metric of the pseudo-Hermitian Hamiltonian and its bi-orthonormal basis of system states are deduced.