Disappearing Q operator
Abstract
In the Schroedinger formulation of nonHermitian quantum theories a positivedefinite metric operator {eta}{identical_to}e{sup 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 nonHermitian quantum theories: the Swanson model, a nonHermitian transform of the simple harmonic oscillator, and the wrongsign quartic oscillator, which has been shown to be equivalent to a conventional asymmetric quartic oscillator.
 Authors:
 Physics Department, Imperial College, London, SW7 2AZ (United Kingdom)
 Publication Date:
 OSTI Identifier:
 21010936
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.025023; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ASYMMETRY; FIELD OPERATORS; HARMONIC OSCILLATORS; INTEGRALS; PROBABILISTIC ESTIMATION; QUANTUM FIELD THEORY; QUANTUM MECHANICS; SCHROEDINGER EQUATION; TRANSFORMATIONS
Citation Formats
Jones, H. F., and Rivers, R. J. Disappearing Q operator. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.025023.
Jones, H. F., & Rivers, R. J. Disappearing Q operator. United States. doi:10.1103/PHYSREVD.75.025023.
Jones, H. F., and Rivers, R. J. Mon .
"Disappearing Q operator". United States.
doi:10.1103/PHYSREVD.75.025023.
@article{osti_21010936,
title = {Disappearing Q operator},
author = {Jones, H. F. and Rivers, R. J.},
abstractNote = {In the Schroedinger formulation of nonHermitian quantum theories a positivedefinite metric operator {eta}{identical_to}e{sup 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 nonHermitian quantum theories: the Swanson model, a nonHermitian transform of the simple harmonic oscillator, and the wrongsign quartic oscillator, which has been shown to be equivalent to a conventional asymmetric quartic oscillator.},
doi = {10.1103/PHYSREVD.75.025023},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}

The qphasedifference operator and twomode qcoherent states
In this paper, we introduce unitary and Hermitian phasedifference operators for the two modes of the electromagnetic field in the qdeformed case. The qcreation and annihilation operators of phasedifference quanta are given, and the algebraic properties of some operators in phase space are discussed. The phasedifference properties of twomode qcoherent states are investigated. {copyright} {ital 1997 American Institute of Physics.} 
Production of four hevy quarks and bound states in the processes e{sup +}e{sup } {yields} Q + {bar Q}{prime} + Q{prime} + {bar Q} and e{sup +}e{sup } {yields} (Q{bar Q}{prime}) + Q{prime} + {bar Q} at the Z{sup 0}boson pole
In the framework of perturbative (QCD) and the nonrelativistic model of heavy quarkonium, the cross sections for the production of four heavy quarks in e{sup +}e{sup {minus}} annihilation and the cross sections for the associative production of 1S and 2Swave (Q{bar Q}{prime}) mesons in the process e{sup +}e{sup {minus}} {yields} (Q{bar Q}{prime}) + Q{prime} + {bar Q} are calculated. The number of {Lambda}{sub be} hyperons expected for LEP experiments is estimated using the assumption of quarkhadron duality. The fragmentation functions of the b quark into the B{sub c}(B{sub c}*) meson and of the c and b quarks into {eta}{sub c}({Psi})more »