The unitary irreducible representations of SU(2,1)

• Published in: Journal of mathematical physics 1990-07, Vol.31 (7), p.1576-1586
• Main Authors: Bars, Itzhak, Teng, Zhong‐jian
• Format: Article
• Language: English
• Subjects: 645300 - High Energy Physics- Particle Invariance Principles & Symmetries; 645400 - High Energy Physics- Field Theory; 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics; CASIMIR OPERATORS; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPOSITE MODELS; DIAGRAMS; Exact sciences and technology; EXTENDED PARTICLE MODEL; FIELD THEORIES; IRREDUCIBLE REPRESENTATIONS; LIE GROUPS; Mathematical methods in physics; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PARTICLE MODELS; Physics; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM NUMBERS; QUARK MODEL; STRING MODELS; SU GROUPS; SU-2 GROUPS; SYMMETRY; SYMMETRY GROUPS; UNITARY SYMMETRY
• ISSN: 0022-2488; 1089-7658
• DOI: 10.1063/1.528698

This paper analyzes the irreducible unitary representations of SU(2,1) in a basis labeled as ‖p, q; j m y〉, where p,q correspond to quantum numbers associated with the quadratic and cubic Casimir operators, j,m label states of the SU(2) subgroup, and 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 (j,y) plot for fixed values of p,q. A (p,q) plot is also provided that indicates the allowed values of these quantum numbers.