Bicoherent-state path integral quantization of a non-hermitian hamiltonian

F. Bagarello, Joshua Feinberg

Research output: Contribution to journalArticlepeer-review


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 languageAmerican English
Article number168313
JournalAnnals of Physics
StatePublished - Nov 2020


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

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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