Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials

Physics and Mathematics of Nonlinear Phenomena 2013

Aquilanti, V.^1 ; Marinelli, D.^2 ; Marzuoli, A.^3

Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, via Elce di Sotto 8, 06123 Perugia, Italy^1

Dipartimento di Fisica, Università di Pavia, INFN Sezione di Pavia, via Bassi 6, 27100 Pavia, Italy^2

Dipartimento di Matematica 'F Casorati', Università di Pavia, INFN Sezione di Pavia, via Ferrata 1, 27100 Pavia, Italy^3

关键词: Angular momentum operators;    Automorphism groups;    Comparative analysis;    Discrete polynomials;    Generalized recoupling coefficient;    Hierarchical structures;    Quadratic algebras;    Symmetric coupling;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012001/pdf
DOI  :  10.1088/1742-6596/482/1/012001

来源: IOP

【 摘 要 】

Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schrodinger-like equation which provides a semiclassical Hamiltonian picture of the evolution of a 'quantum of space', as shown by the authors in [1]. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed.