Formalism of a harmonic oscillator in the future-included complex action theory
| Autor: | Holger Bech Nielsen, Keiichi Nagao |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
High Energy Physics - Theory
Physics Quantum Physics Annihilation Angular frequency FOS: Physical sciences General Physics and Astronomy Hermitian matrix High Energy Physics - Theory (hep-th) Effective field theory Coherent states Quantum Physics (quant-ph) Complex number Eigenvalues and eigenvectors Harmonic oscillator Mathematical physics |
| Zdroj: | Nagao, K & Nielsen, H B 2019, ' Formalism of a harmonic oscillator in the future-included complex action theory ', Progress of Theoretical and Experimental Physics, vol. 2019, no. 7, 073B01 . https://doi.org/10.1093/ptep/ptz047 |
| DOI: | 10.1093/ptep/ptz047 |
| Popis: | 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 $\hat{H}$, in which a mass $m$ and an angular frequency $\omega$ are taken to be complex numbers. In order for the model to be sensible some restrictions on $m$ and $\omega$ are required. We draw a phase diagram in the plane of the arguments of $m$ and $\omega$, 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 $\hat{H}$ and $\hat{H}^\dag$, and coherent states. They are normalized in a modified inner product $I_Q$, with respect to which the Hamiltonian $\hat{H}$ 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 $I_Q$. The generic solution to the model is found to be the ``ground'' state. Finally we discuss what the solution implies. Comment: Latex 42 pages, 3 figures, typos corrected, presentation improved, the final version to appear in Prog.Theor.Exp.Phys |
| Databáze: | OpenAIRE |
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