The Wigner supermultiplet model revisited. Analytical determination of internal labelling operators by means of contracted Casimir operators

Abstract

We prove that the missing label operators for the state labelling problem in the Wigner supermultiplet model su(2)×su(2) � su(4) can be solved naturally without explicitly using enveloping algebras. Considering a contraction of Lie algebras naturally associated to the reduction chain su(2)×su(2) ,! su(4), we recover the Moshinsky-Nagel operators as functions of the Casimir operators of su(4), the spin-isospin subalgebra and the corresponding inhomogeneous contraction