The Jordan–Schwinger representations of Cayley–Klein groups. I. The orthogonal groups

DOI10.1063/1.528781zbMath0701.22009OpenAlexW1997927699MaRDI QIDQ3478634

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Publication date: 1990

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

Full work available at URL: https://doi.org/10.1063/1.528781

zbMATH Keywords

orthogonal groupsmatrix elementscreation and annihilation operatorsFock statesCayley-Klein groupsJordan-Schwinger representations

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) Coherent states (81R30)

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The Gel’fand–Tsetlin representations of the unitary Cayley–Klein algebras ⋮ The Gel’fand–Tsetlin representations of the orthogonal Cayley–Klein algebras ⋮ Contractions of the irreducible representations of the quantum algebras suq(2) and soq(3) ⋮ On the oscillator realization of conformal U(2, 2) quantum particles and their particle-hole coherent states ⋮ Superintegrability on the Dunkl oscillator model in three-dimensional spaces of constant curvature ⋮ The Jordan–Schwinger representations of Cayley–Klein groups. II. The unitary groups ⋮ The Jordan–Schwinger representations of Cayley–Klein groups. III. The symplectic groups ⋮ On the differential equation of first and second order in the Zeon algebra ⋮ Lie–Hamilton systems on curved spaces: a geometrical approach ⋮ Geometry-preserving numerical methods for physical systems with finite-dimensional Lie algebras ⋮ Curvature as an Integrable Deformation ⋮ Behavior of a constrained particle on superintegrability of the two-dimensional complex Cayley-Klein space and its thermodynamic properties

Cites Work

• Casimir operators of groups of motions of spaces of constant curvature
• Theorems on the Jordan–Schwinger representations of Lie algebras
• Introducing division by an ‘‘a’’ number and a new ‘‘b’’ number in particle physics
• Coherent and Incoherent States of the Radiation Field
• On the Contraction of Groups and Their Representations

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