We introduce, for the first time, bicoherent-state path integration as a method for quantizing non-hermitian systems. Bicoherent-state path integrals arise as a natural generalization of ordinary coherent-state path integrals, familiar from hermitian quantum physics. We do all this by working out a concrete example, namely, computation of the propagator of a certain quasihermitian variant of Swanson's model, which is not invariant under conventional PT-transformation. The resulting propagator coincides with that of the propagator of the standard harmonic oscillator, which is isospectral with the model under consideration by virtue of a similarity transformation relating the corresponding hamiltonians. We also compute the propagator of this model in position space by means of Feynman path integration and verify the consistency of the two results. (C) 2020 Elsevier Inc. All rights reserved.

F. Bagarello, Joshua Feinberg (2020). Bicoherent-state path integral quantization of a non-Hermitian Hamiltonian. ANNALS OF PHYSICS, 422, 168313 [10.1016/j.aop.2020.168313].

Bicoherent-state path integral quantization of a non-Hermitian Hamiltonian

F. Bagarello
;
2020-11-01

Abstract

We introduce, for the first time, bicoherent-state path integration as a method for quantizing non-hermitian systems. Bicoherent-state path integrals arise as a natural generalization of ordinary coherent-state path integrals, familiar from hermitian quantum physics. We do all this by working out a concrete example, namely, computation of the propagator of a certain quasihermitian variant of Swanson's model, which is not invariant under conventional PT-transformation. The resulting propagator coincides with that of the propagator of the standard harmonic oscillator, which is isospectral with the model under consideration by virtue of a similarity transformation relating the corresponding hamiltonians. We also compute the propagator of this model in position space by means of Feynman path integration and verify the consistency of the two results. (C) 2020 Elsevier Inc. All rights reserved.
nov-2020
F. Bagarello, Joshua Feinberg (2020). Bicoherent-state path integral quantization of a non-Hermitian Hamiltonian. ANNALS OF PHYSICS, 422, 168313 [10.1016/j.aop.2020.168313].
File in questo prodotto:
File Dimensione Formato  
bicoherent path integral-final-revised 23.7.2020.pdf

accesso aperto

Descrizione: the paper
Tipologia: Pre-print
Dimensione 350.25 kB
Formato Adobe PDF
350.25 kB Adobe PDF Visualizza/Apri
1-s2.0-S0003491620302475-main.pdf

Solo gestori archvio

Tipologia: Versione Editoriale
Dimensione 609.82 kB
Formato Adobe PDF
609.82 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/584353
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 3
social impact