2014/02/21 by E. Celeghini, Celeghini, E., M. A. del Olmo +4
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1402.5217
21 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1307.7380
arxiv created 2014/02/21 · openalex publication_date 2014/02/21 · arxiv updated 2014/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A symmetry SU(2,2) group in terms of ladder operators is presented for the Jacobi polynomials, Jn(α,β)(x), and the Wigner dj-matrices where the spins j=n+(α+β)/2 integer and half-integer are considered together. A unitary irreducible representation of SU(2,2) is constructed and subgroups of physical interest are discussed. The Universal Enveloping Algebra of su(2,2) also allows to construct group structures (SU(1,1), SO(3,2), Spin(3,2)) whose representations separate integers and half-integers values of the spin j. Appropriate L2--functions spaces are realized inside the support spaces of all these representations. Operators acting on these L2-functions spaces belong thus to the corresponding Universal Enveloping Algebra.