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

Journal Article · Thu Oct 31 23:00:00 EST 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526740· OSTI ID:5219294

Deenen, J; Quesne, C

Both non-Hermitian Dyson and Hermitian Holstein--Primakoff representations of the Sp(2d,R) algebra are obtained when the latter is restricted to a positive discrete series irreducible representation . For such purposes, some results for boson representations, recently deduced from a study of the Sp(2d,R) partially coherent states, are combined with some standard techniques of boson expansion theories. The introduction of Usui operators enables the establishment of useful relations between the various boson representations. Two Dyson representations of the Sp(2d,R) algebra are obtained in compact form in terms of ..nu.. = d(d+1)/2 pairs of boson creation and annihilation operators, and of an extra U(d) spin, characterized by the irreducible representation (lambda/sub 1/xxxlambda/sub d/). In contrast to what happens when lambda/sub 1/ = xxx = lambda/sub d/ = lambda, it is shown that the Holstein--Primakoff representation of the Sp(2d,R) algebra cannot be written in such a compact form for a generic irreducible representation. Explicit expansions are, however, obtained by extending the Marumori, Yamamura, and Tokunaga method of boson expansion theories. The Holstein--Primakoff representation is then used to prove that, when restricted to the Sp(2d,R) irreducible representation , the dn-dimensional harmonic oscillator Hamiltonian has a U(..nu..) x SU(d) symmetry group.

• Research Organization: Service de Physique Theorique et Mathematique CP 229, Universite Libre de Bruxelles, Bd. du Triomphe, B 1050 Brussels, Belgium
• OSTI ID: 5219294
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:11; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

653007* -- Nuclear Theory-- Nuclear Models-- (-1987)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANNIHILATION OPERATORS
BOSON EXPANSION
COLLECTIVE MODEL
CREATION OPERATORS
GROUP THEORY
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICS
NUCLEAR MODELS
QUANTUM OPERATORS
SP GROUPS
SU GROUPS
SYMMETRY
SYMMETRY GROUPS