Coherency of su(1,1)-Barut–Girardello type and entanglement for spherical harmonics

DOI10.1063/1.3129491zbMath1187.81157OpenAlexW1963917730MaRDI QIDQ3565252

Hossein Fakhri, A. Dehghani

Publication date: 3 June 2010

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3129491

zbMATH Keywords

spherical harmonicsirreducible representationsBarut--Girardello coherent statessu(1,1) Lie algebra

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Coherent states (81R30)

Related Items

Two-qutrit entangled \(f\)-coherent states, Spherical harmonics \(Y_l^m(\theta, \phi)\): positive and negative integer representations of \(\mathrm{su}(1,1)\) for \(l - m\) and \(l + m\), GENERALIZED COHERENT STATES FOR THE SPHERICAL HARMONICS $Y_{m}^{m}(\theta,\phi)$, Nonclassical properties and polarization degree of photon-subtracted entangled nonlinear coherent states, Superposition of two-mode ``near coherent states: non-classicality and entanglement, Entanglement dynamics of a nano-mechanical resonator coupled to a central qubit, New generalized coherent states arising from generating functions: a novel approach

Cites Work

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• Generalized coherent states for a relativistic model of the linear oscillator in a homogeneous external field
• Coherent states on the group SL(2,R). Series of coherent states and automorphic forms; Mellin transforms
• Quantum \(SU(1,1)\)-harmonic oscillator
• The \(q\)-deformed oscillator representations and their coherent states of the \(su(1,1)\) algebra
• New 'coherent' states associated with non-compact groups
• Coherent states for arbitrary Lie group
• Entangled coherent states for systems withSU(2) andSU(1,1) symmetries
• Temporally stable coherent states for infinite well and Pöschl–Teller potentials
• A remarkable property of spherical harmonics
• The Clebsch–Gordan problem of the SL(2,R) coherent states
• Coherent states on the m-sheeted covering group of SU(1,1)
• Coherent states for systems with discrete and continuous spectrum
• Hilbert spaces of analytic functions for the SL(2,R) coherent states and a class of associated integral transforms
• Maximal violation of Bell inequalities for mixed states
• BARUT–GIRARDELLO COHERENT STATES CONSTRUCTED BY Y_{m m}(θ,φ) AND Y_{m+1 m}(θ,φ) FOR A FREE PARTICLE ON THE SPHERE
• su(1, 1)-Barut–Girardello coherent states for Landau levels
• Coherent states and annihilation–creation operators associated with the irreducible unitary representations of 𝔰𝔲(1,1)
• Coherent states of SU(l, 1) groups
• KLAUDER–PERELOMOV AND GAZEAU–KLAUDER COHERENT STATES FOR SOME SHAPE INVARIANT POTENTIALS
• Continuous-Representation Theory. I. Postulates of Continuous-Representation Theory
• Coherent and Incoherent States of the Radiation Field
• New Theorems about Spherical Harmonic Expansions and SU(2)
• Equivalence of Semiclassical and Quantum Mechanical Descriptions of Statistical Light Beams