Quantization of the classical SL(2,R) system and representations of SL(2,R) group

DOI10.1063/1.530016zbMath0794.22017OpenAlexW2145056647MaRDI QIDQ3141387

Mikhail S. Plyushchay

Publication date: 13 July 1994

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

Full work available at URL: https://doi.org/10.1063/1.530016

zbMATH Keywords

quantizationunitary irreducible representationsdiscrete seriesuniversal covering groupprincipal seriesbrackets

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (10)

(2 + 1)D exotic Newton-Hooke symmetry, duality and projective phase ⋮ (2+1)-dimensional models of relativistic particles with curvature and torsion ⋮ Conformal mechanics ⋮ Massless particle in 2d spacetime with constant curvature ⋮ Monopole Chern-Simons term: charge-monopole system as a particle with spin. ⋮ Geometry of \(2\)d spacetime and quantization of particle dynamics ⋮ A relativistic particle in the Liouville field ⋮ Hidden symmetry and (super)conformal mechanics in a monopole background ⋮ Aspects of coherent states of nonlinear algebras ⋮ Quantum mechanics on noncommutative Riemann surfaces

Cites Work

• General concept of quantization
• Irreducible unitary representations of the Lorentz group
• Noncompact Lie-algebraic approach to the unitary representations of SU∼(1,1): Role of the confluent hypergeometric equation
• Unitary Representations of the Lorentz Groups: Reduction of the Supplementary Series under a Noncompact Subgroup
• Unitary Representations of the Group O(2, 1) in an O(1, 1) Basis

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