Coherent states of the real symplectic group in a complex analytic parametrization. II. Annihilation-operator coherent states

Journal Article · Fri Feb 28 23:00:00 EST 1986 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.527194· OSTI ID:6326403

Quesne, C

In the present series of papers, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations , encountered in physical applications, are analyzed in detail with special emphasis on those of Sp(4,R) and Sp(6,R). The present paper discusses the annihilation-operator coherent states, i.e., the eigenstates of the noncompact lowering generators corresponding to complex eigenvalues. These states generalize the coherent states introduced by Barut and Girardello for Sp(2,R), and later on extended by Deenen and Quesne to the Sp(2d,R) irreducible representations of the type <(lambda+n/2)/sup d/>. When lambda1,...,lambda/sub d/ are not all equal, it was shown by Deenen and Quesne that the eigenvalues do not completely specify the eigenstates of the noncompact lowering generators.

• Research Organization: Physique Theorique et Mathematique CP 229, Universite Libre de Bruxelles, Boulevard du Triomphe, B 1050 Brussels, Belgium
• OSTI ID: 6326403
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 27:3; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANNIHILATION OPERATORS
CREATION OPERATORS
FIELD THEORIES
GROUP THEORY
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICS
NUCLEAR MODELS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SP GROUPS
SYMMETRY
SYMMETRY GROUPS