The disappearing $Q$ operator
| dc.creator | Jones, H. F. | |
| dc.creator | Rivers, R. J. | |
| dc.date | 2006-12-11 | |
| dc.date.accessioned | 2026-07-07T11:59:31Z | |
| dc.date.available | 2026-07-07T11:59:31Z | |
| dc.description | In the Schroedinger formulation of non-Hermitian quantum theories a positive-definite metric operator $η\equiv e^{-Q}$ must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent Hermitian theory, by means of a similarity transformation. If, however, quantum mechanics is formulated in terms of functional integrals, we show that the $Q$ operator makes only a subliminal appearance and is not needed for the calculation of expectation values. Instead, the relation to the Hermitian theory is encoded via the external source $j(t)$. These points are illustrated and amplified for two non-Hermitian quantum theories: the Swanson model, a non-Hermitian transform of the simple harmonic oscillator, and the wrong-sign quartic oscillator, which has been shown to be equivalent to a conventional asymmetric quartic oscillator. | |
| dc.description | 14 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/hep-th/0612093 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0612093 | |
| dc.identifier | Phys.Rev.D75:025023,2007 | |
| dc.identifier | doi:10.1103/PhysRevD.75.025023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/206591 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Physics | |
| dc.title | The disappearing $Q$ operator | |
| dc.type | text |