Boson representations of the real symplectic group and their applications to the nuclear collective model

DOI10.1063/1.526740zbMath0594.22012OpenAlexW1987863865MaRDI QIDQ3724588

J. Deenen, Christiane Quesne

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1063/1.526740

zbMATH Keywords

discrete series representationsboson representationsnuclear collective modelrepresentations of Sp(n,R)Usui operators

Mathematics Subject Classification ID

Nuclear physics (81V35) 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

Coherent states of the real symplectic group in a complex analytic parametrization. I. Unitary-operator coherent states ⋮ Collective nuclear potential within the microscopic Sp(6,R) model ⋮ Vector-coherent-state theory as a theory of induced representations ⋮ The nuclear collective WSp(6,R) model ⋮ Closed, analytic, boson realizations for Sp(4) ⋮ Induced shift tensors in vector coherent state theory ⋮ A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras ⋮ On the boson–quasifermion realization of the particle–hole SO(2Ω+1) algebra ⋮ Collectivity and geometry. VI. Spectra and shapes in the three-dimensional case ⋮ Fermion realization of the nuclear Sp(6,R) model

Cites Work

• A simple independent-particle system having collective properties
• The discrete series of \(Sp(n,\mathbb{R})\)
• New 'coherent' states associated with non-compact groups
• Coherent states for arbitrary Lie group
• General Theory of Spin-Wave Interactions
• Collective motion in the nuclear shell model. I. Classification schemes for states of mixed configurations
• Excitations in a High Density Electron Gas. I
• On a Hilbert space of analytic functions and an associated integral transform part I
• Representations of the groups Sp(n,R) and Sp(n) in a U(n) basis
• Canonical transformations relating the oscillator and Coulomb problems and their relevance for collective motions
• On the Representations of the Semisimple Lie Groups. II
• Noninvariance Groups in the Second-Quantization Picture and Their Applications
• Linear Canonical Transformations and Their Unitary Representations
• On the Problem of Degeneracy in Quantum Mechanics
• Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet