6533b833fe1ef96bd129c178

RESEARCH PRODUCT

Bicoherent-State Path Integral Quantization of a non-Hermitian Hamiltonian

Fabio BagarelloJoshua Feinberg

subject

High Energy Physics - TheorySwanson modelFOS: Physical sciencesGeneral Physics and AstronomyPT symmetrysymbols.namesakeFeynman diagramHarmonic oscillatorMathematical PhysicsNon-hermitian hamiltoniansMathematical physicsPhysicsQuantum PhysicsQuantization (signal processing)PropagatorMathematical Physics (math-ph)Bicoherent statesHermitian matrixIsospectralHigh Energy Physics - Theory (hep-th)Path integral quantizationPath integral formulationsymbolsPseudo-bosonsQuantum Physics (quant-ph)Hamiltonian (quantum mechanics)

description

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.

yearjournalcountryeditionlanguage
2020-11-01
10.1016/j.aop.2020.168313http://arxiv.org/abs/2001.04955