The state labeling problems for SO(N) in U(N) and U(M) in Sp(2M)
- 1 August 1976
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 17 (8) , 1376-1382
- https://doi.org/10.1063/1.523087
Abstract
It is shown that, in a boson representation, the operators whose eigenvalues serve to label representations of SO(N) in U(N) also serve to label representations of U(M) in Sp(2M). The problem of labeling U(2) in Sp(4) is considered in detail, and it is shown how to find labeling operators with rational eigenvalues, depending, however, on the representation. The solution of this problem is shown to provide a solution of the equivalent problem of the labeling of SO(3) in U(3).Keywords
This publication has 13 references indexed in Scilit:
- Casimir operators of complementary unitary groupsJournal of Mathematical Physics, 1975
- Angular momentum in tensor representations ofU (3)International Journal of Theoretical Physics, 1974
- Numerical computation of scattering phase shifts for a screened Coulomb potentialJournal of Physics A: Mathematical, Nuclear and General, 1974
- On a solution of the U(N)⊃O(N) state labelling problem for two-rowed representationsJournal of Physics A: Mathematical, Nuclear and General, 1974
- The harmonic oscillator: values of the SU(3) invariantsJournal of Physics A: Mathematical, Nuclear and General, 1973
- Irreducible representations of a parafield and the connection of the parafield with usual fieldsInternational Journal of Theoretical Physics, 1973
- The Boson Calculus for the Orthogonal and Symplectic GroupsJournal of Mathematical Physics, 1971
- Noninvariance Groups in the Second-Quantization Picture and Their ApplicationsJournal of Mathematical Physics, 1970
- Group theory of harmonic oscillators (II). The integrals of Motion for the quadrupole-quadrupole interactionNuclear Physics, 1961
- Group theory of harmonic oscillatorsNuclear Physics, 1960