The unitary irreducible representations of SU(2,1)

Journal Article · Sun Jul 01 00:00:00 EDT 1990 · Journal of Mathematical Physics (New York); (USA)

DOI:https://doi.org/10.1063/1.528698· OSTI ID:7093511

Bars, I; Teng, Z ^[1]

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1. Physics Department, University of Southern California, Los Angeles, California 90089-0484 (US)

This paper analyzes the irreducible unitary representations of SU(2,1) in a basis labeled as {vert bar}{ital p}, {ital q}; {ital jmy}{r angle}, where {ital p},{ital q} correspond to quantum numbers associated with the quadratic and cubic Casimir operators, {ital j},{ital m} label states of the SU(2) subgroup, and {ital y} labels the quantum number with respect to the U(1) subgroup. All the irreducible representations are found and the allowed range of these quantum numbers for each representation are given. The results are expressed in the form of diagrams that show the allowed values in a ({ital j},{ital y}) plot for fixed values of {ital p},{ital q}. A ({ital p},{ital q}) plot is also provided that indicates the allowed values of these quantum numbers.

• DOE Contract Number: FG03-84ER40168
• OSTI ID: 7093511
• Journal Information: Journal of Mathematical Physics (New York); (USA), Journal Name: Journal of Mathematical Physics (New York); (USA) Vol. 31:7; ISSN JMAPA; ISSN 0022-2488
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CASIMIR OPERATORS
COMPOSITE MODELS
DIAGRAMS
EXTENDED PARTICLE MODEL
FIELD THEORIES
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
PARTICLE MODELS
QUANTUM NUMBERS
QUARK MODEL
STRING MODELS
SU GROUPS
SU-2 GROUPS
SYMMETRY
SYMMETRY GROUPS
UNITARY SYMMETRY