Closed, analytic, boson realizations for Sp(4)
Journal Article
·
· J. Math. Phys. (N.Y.); (United States)
The problem of determing a boson realization for an arbitrary irrep of the unitary simplectic algebra Sp(2d-italic) (or of the corresponding discrete unitary irreps of the unbounded algebra Sp(2d-italic,R-italic)) has been solved completely in recent papers. This solution is not known in closed analytic form except for d-italic = 1 and for special classes of irreps for d-italic>1. A different method of obtaining a boson realization that solves the full problem for Sp(4) is described. The method utilizes the chain Sp(2d-italic)containsSU(2) x SU(2) x xxx x SU(2) (d-italic times), which, for d-italic> or =4, does not provide a complete set of quantum numbers. Though a simple solution of the missing label problem can be given, this solution does not help in the construction of a mapping algorithm for general d-italic.
- Research Organization:
- Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396
- OSTI ID:
- 5368579
- Journal Information:
- J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 27:8; ISSN JMAPA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
645400 -- High Energy Physics-- Field Theory
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
ALGORITHMS
BOSON EXPANSION
DIMENSIONS
FIELD THEORIES
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL LOGIC
MATHEMATICS
MECHANICS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM NUMBERS
SP GROUPS
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
U GROUPS
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
ALGORITHMS
BOSON EXPANSION
DIMENSIONS
FIELD THEORIES
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL LOGIC
MATHEMATICS
MECHANICS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM NUMBERS
SP GROUPS
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
U GROUPS