Coherent states for the harmonic oscillator representations of the orthosymplectic supergroup Osp(1/2N,R)

DOI10.1063/1.528189zbMath0647.17016OpenAlexW2067271286MaRDI QIDQ3791314

H. A. Schmitt, A. Baha Balantekin, B. R. Barrett

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1063/1.528189

zbMATH Keywords

coherent statesLie superalgebrasLie supergroupsharmonic oscillator representationOsp(1/2N,\({bbfR})\)

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) Superalgebras (17A70) Graded Lie (super)algebras (17B70)

Related Items

On the supersymplectic homogeneous superspace underlying the OSp(1/2) coherent states ⋮ Supercoherent states, super-Kähler geometry and geometric quantization ⋮ Character expansions for the orthogonal and symplectic groups ⋮ Transformations of some induced osp(3/2) modules in an so(3)⊕sp(2) basis ⋮ Path-integral formalism for the supercoherent states ⋮ Supersymmetry and supercoherent states of a nonrelativistic free particle ⋮ Coherent states for the noncompact supergroups Osp(2/2N,R) ⋮ On generalized coherent states with maximal symmetry for the harmonic oscillator ⋮ A unified and complete construction of all finite dimensional irreducible representations of gl(2∣2) ⋮ Supercoherent-state representation of the OSP(2,1) superalgebra ⋮ Completeness and geometry of Schrödinger minimum uncertainty states ⋮ Parastatistics, supersymmetry and parasupercoherent states ⋮ On chains of orthosymplectic Lie superalgebras and the n-dimensional quantum harmonic oscillator ⋮ Representations of quantum superalgebra U q[gl(2|1) in a coherent state basis and generalization] ⋮ $Sp(4; \mathbb{R})$ squeezing for Bloch four-hyperboloid via the non-compact Hopf map

Cites Work

• Unitary representations of noncompact supergroups
• Coherent states and symmetric spaces
• New 'coherent' states associated with non-compact groups
• Relation between the supertableaux of the supergroups OSP(2‖2) and SU(1‖2)
• Erratum: Semisimple Lie algebras
• The graded Lie groups SU(2,2/1) and OSp(1/4)

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