Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Mathematical Physics

Generalized coherent states for a three-dimensional relativistic model of the oscillator

Natig M. Atakishiyev, R. M. Mir‐Kasimov

Published Jul 1, 1989• 2 citations
Publisher

Abstract

The SU(1,1) coherent states for a relativistic model of the oscillator in the configurational r representation are considered. Classical equations of motion in the generalized phase space are obtained with the help of the path integral for the transition amplitude between SU(1,1) coherent states. It is shown that the use of the semiclassical Bohr–Sommerfeld quantization rule yields the exact expression for the energy levels.

DOI
10.1063/1.528296

Related papers

Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator

Sh. M. Nagiyev, E. I. Jafarov, Messoud Efendiyev

The SU(1,1) coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU(1,1) coherent states is given. Classical equations of the motion in the generalized curved phase space are obtained. It is shown that the use of quasiclassical Bohr–Sommerfeld quantization rule yields the exact expression for the energy spectrum.

arXiv:math-ph/0702003•Communications in Theoretical Physics•Feb 1, 2008•2 citations

Path integral in the representation of SU(2) coherent state and classical dynamics in a generalized phase space

Hiroshi Kuratsuji, T. Suzuki

Path integral in the representation of coherent state for the simplest semisimple Lie group SU(2) and its classical consequences are investigated. Using the completeness relation of the coherent state, we derive a path integral expression for the transition amplitude which connects a pair of SU(2) coherent states. In the classical limit we arrive at a canonical equation of motion in a ’’curved phase space’’ (two-dimensional sphere) which reproduces the ordinary Euler’s equation of a rigid body when applied to a rotator.

Journal of Mathematical Physics•Mar 1, 1980•127 citations

Path integral formalism for SUq(2) coherent states

Renshan Gong

A path integral formulation in the representation of coherent states for the quantum group SU q (2) is introduced. An expression for the transition amplitude connecting two SU q (2) coherent states is constructed, and the corresponding canonical equations of motion are also derived.

Journal of Physics A Mathematical and General•Oct 7, 1992•6 citations

Large- N phase-integral approximation for SU(1,1) coherent states

Christopher C. Gerry, James B. Togeas, S. J. Silverman

From our recently developed representation of the path integral in terms of coherent states of the dynamical group SU(1,1), we obtain the semiclassical limit as a large-$N$ limit. Specifically, the parameter $k=\frac{1}{2}(l+\frac{N}{2})$ which labels the relevant SU(1,1) representations plays the role of ${\ensuremath{\hbar}}^{\ensuremath{-}1}$. A phase-integral quantization rule is given and used to calculate the energy eigenvalues for various isotropic anharmonic oscillators. We obtain results comparable to the first-order JWKB calculations even at $N=1$.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Oct 15, 1983•18 citations

Path integral for coherent states of the dynamical group SU(1,1)

Christopher C. Gerry, S. J. Silverman

Path integrals over coherent states of the dynamical group (noninvariance group) SU(1,1) are constructed. From the continuous limit the relevant classical dynamics is extracted and is shown to take place in a curved phase space of the form of a Lobachevskii plane. Applications are made to the harmonic oscillator, a model of superfluid helium, the Morse oscillator, and the hydrogen atom. It is shown that when SU(1,1) is the relevant dynamical group the motion will appear oscillator-like on the Lobachevskii plane.

Journal of Mathematical Physics•Nov 1, 1982•67 citations

Path integral formalism for Osp(1/2, R) coherent states

H. A. Schmitt, A. Mufti

A path integral formulation in the representation of coherent states for the non-compact supergroup Osp(1/2, R) is introduced. An expression for the transition amplitude connecting two Osp(1/2, R) coherent states is constructed, and the corresponding canonical equations of motion derived. A set of generalized Poisson brackets is introduced and interpreted.

Journal of Physics A Mathematical and General•Aug 7, 1991•7 citations
The SU(1,1) coherent states for a relativistic model of the oscillator in the configurational r representation are considered. Classical equations of motion in the generalized phase space are obtained with the help of the path integral for the transition amplitude between SU(1,1) coherent states. It is shown that the use of the semiclassical Bohr–Sommerfeld quantization rule yields the exact expression for the energy levels.
Path integral in the representation of coherent state for the simplest semisimple Lie group SU(2) and its classical consequences are investigated. Using the completeness relation of the coherent state, we derive a path integral expression for the transition amplitude which connects a pair of SU(2) coherent states. In the classical limit we arrive at a canonical equation of motion in a ’’curved phase space’’ (two-dimensional sphere) which reproduces the ordinary Euler’s equation of a rigid body when applied to a rotator.
From our recently developed representation of the path integral in terms of coherent states of the dynamical group SU(1,1), we obtain the semiclassical limit as a large-NNN limit. Specifically, the parameter k=12(l+N2)k=\frac{1}{2}(l+\frac{N}{2})k=21​(l+2N​) which labels the relevant SU(1,1) representations plays the role of ${\ensuremath{\hbar}}^{\ensuremath{-}1}$. A phase-integral quantization rule is given and used to calculate the energy eigenvalues for various isotropic anharmonic oscillators. We obtain results comparable to the first-order JWKB calculations even at N=1N=1N=1.
Path integrals over coherent states of the dynamical group (noninvariance group) SU(1,1) are constructed. From the continuous limit the relevant classical dynamics is extracted and is shown to take place in a curved phase space of the form of a Lobachevskii plane. Applications are made to the harmonic oscillator, a model of superfluid helium, the Morse oscillator, and the hydrogen atom. It is shown that when SU(1,1) is the relevant dynamical group the motion will appear oscillator-like on the Lobachevskii plane.