## 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 quasi-hermitian 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.

Original language | English |
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Article number | 168313 |

Journal | Annals of Physics |

Volume | 422 |

DOIs | |

State | Published - Nov 2020 |

### Bibliographical note

Funding Information:This collaboration was initiated when the authors met at the International Centre for Theoretical Sciences (ICTS) during a visit for participating in the program ‘Non-Hermitian Physics - PHHQP XVIII’ (Code: ICTS/nhp2018/06). This work was partially supported by the University of Palermo and by the Gruppo Nazionale di Fisica Matematica of Indam , and by the Israel Science Foundation (grant No. 2040/17 ). J.F. also thanks the University of Palermo for financial support via CORI.

Funding Information:

This collaboration was initiated when the authors met at the International Centre for Theoretical Sciences (ICTS) during a visit for participating in the program ?Non-Hermitian Physics - PHHQP XVIII? (Code: ICTS/nhp2018/06). This work was partially supported by the University of Palermo and by the Gruppo Nazionale di Fisica Matematica of Indam, and by the Israel Science Foundation (grant No. 2040/17). J.F. also thanks the University of Palermo for financial support via CORI.

Publisher Copyright:

© 2020 Elsevier Inc.

## Keywords

- Bicoherent states
- Non-hermitian hamiltonians
- PT symmetry
- Path integral quantization
- Pseudo-bosons
- Swanson model

## ASJC Scopus subject areas

- Physics and Astronomy (all)