The Clebsch–Gordan coefficients of the three-dimensional Lorentz algebra in the parabolic basis

DOI10.1063/1.525745zbMath0513.22014OpenAlexW2060285723MaRDI QIDQ3658216

Kurt Bernardo Wolf, Debabrata Basu

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1063/1.525745

zbMATH Keywords

tensor productsClebsch-Gordan coefficientsLorentz groupLorentz algebrahypergometric functionsparabolic basisself-adjoint irreducible representation

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70)

Related Items (10)

Lie algebras for systems with mixed spectra. I. The scattering Pöschl–Teller potential ⋮ The covariant linear oscillator and generalized realization of the dynamical SU(1,1) symmetry algebra ⋮ Factorization method and new potentials with the oscillator spectrum ⋮ Quantum superintegrable Zernike system ⋮ The Schwarzian theory -- a Wilson line perspective ⋮ Laguerre functions and representations of \(su\)(1,1) ⋮ Development of Linear Canonical Transforms: A Historical Sketch ⋮ The Gel’fand realization and the generating function of the Clebsch–Gordan coefficients of SL(2,R) in the hyperbolic basis ⋮ Are the spectra of geometrical operators in loop quantum gravity really discrete? ⋮ Quantum phase space for the one-dimensional hydrogen atom on the hyperbola

Cites Work

• Complex angular momenta and the groups \(\mathrm{SU}(1,1)\) and \(\mathrm{SU}(2)\)
• A general study of the Wigner coefficients of \(\mathrm{SU}(1,1)\)
• The Plancherel formula for the universal covering group of SL(R, 2)
• Irreducible unitary representations of the Lorentz group
• The master analytic function and the Lorentz group. III. Coupling of continuous representations of O(2,1)
• On the Kronecker Products of Irreducible Representations of the 2 × 2 Real Unimodular Group. I
• Canonical transforms. IV. Hyperbolic transforms: Continuous series of SL(2,R) representations
• The unitary irreducible representations of SL(2, R) in all subgroup reductions
• Clebsch-Gordan problem and coefficients for the three-dimensional Lorentz group in a continuous basis. I
• Singular potentials in nonrelativistic quantum mechanics
• Uniformly bounded representations of the universal covering group of ${\text{SL}}\left( {2,\,R} \right)$
• On the wigner coefficients of the three-dimensional Lorentz group
• Linear Canonical Transformations and Their Unitary Representations
• New forms for the representations of the three-dimensional Lorentz group

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