Projection operator method and Q-analog of angular momentum theory

Abstract

Quantum algebras were introduced at first in Refs.[1,2]. Then this concept was developed in details in Refs.[3,4] and in the papers of other authors (see for example [5–11] and the papers cited there). Because of deep analogy consisting between quantum and usual Lie algebras which is reflected in the fact that the quantum algebra A q (l,r) of order l and rank r transforms into usual Lie algebra A(l,r) in the limit q→1 a number of notations and theorems of the theory of Lie algebra representations can be transferred onto quantum algebras. In particular as it was shown in Refs [5–17] the q-analogs of well known quantities of Wigner-Racah algebra (WRA) (3j, 6j, 9j-symbols etc.) can be introduced. The detail investigation of the representation of quantum algebras was begun with the simplest quantum algebra SU q (2) that is a q-analog of the an-gular momentum theory (AMT) [18–21].