2019/02/04 by Keiichi Nagao, Holger Bech Nielsen, Nagao, Keiichi +2
Computer Science · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Dynamics and Pattern Formation #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.1902.01424
Latex 42 pages, 3 figures, typos corrected, presentation improved, the final version to appear in Prog.Theor.Exp.Phys
openalex publication_date 2019/02/04 · arxiv created 2019/06/18 · arxiv updated 2019/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a special representation of complex action theory that we call ``future-included'', we study a harmonic oscillator model defined with a non-normal Hamiltonian H, in which a mass m and an angular frequency ω are taken to be complex numbers. In order for the model to be sensible some restrictions on m and ω are required. We draw a phase diagram in the plane of the arguments of m and ω, according to which the model is classified into several types. In addition, we formulate two pairs of annihilation and creation operators, two series of eigenstates of the Hamiltonians H and H^†, and coherent states. They are normalized in a modified inner product IQ, with respect to which the Hamiltonian H becomes normal. Furthermore, applying to the model the maximization principle that we previously proposed, we obtain an effective theory described by a Hamiltonian that is Q-Hermitian, i.e. Hermitian with respect to the modified inner product IQ. The generic solution to the model is found to be the ``ground'' state. Finally we discuss what the solution implies.