Abstract
The Clebsch-Gordan (CG) coefficient coupling two positive discrete series or two negative discrete series of irreducible unitary representations (IUR) of SU(1,1) are shown to be identical to SU(2) CG coefficients. The transformations changing the indices of the SU(1,1) CG coefficients into those of the identical SU(2) CG coefficients are derived and shown to transform the SU(2) CG coefficients into SU(1,1) CG coefficients. The associated phases are discussed. General index transformations are derived and used to generate SU(2) CG coefficient symmetries, among which are some of the more abstract Regge symmetries. A simple invariance property of the intermediate SU(1,1) CG coefficients is at the base of the symmetries. The demonstrations are carried out with coexistent IUR of the tensor product groups SU(1,1)(+)SU(1,1) and SU(2)(+)SU(2) embedded in a simple encompassing group structure, the most degenerate discrete IUR of SU(2,2).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.