Automated angular momentum recoupling algebra

Analytical Scheme Calculations of Angular Momentum Coupling and Recoupling Coefficients

We investigate the Scheme programming language opportunities to analytically calculate the ClebschÄGordan coefˇcients, Wigner 6j and 9j symbols, and general recoupling coefˇcients that are used in the quantum theory of angular momentum. The considered coefˇcients are calculated by a direct evaluation of the sum formulas. The calculation results for large values of quantum angular momenta were c...

Angular Momentum, Quaternion, Octonion, and Lie-super Algebra Osp(1,2) *

We will derive both quaternion and octonion algebras as the Clebsch-Gordan algebras based upon the su(2) Lie algebra by considering angular momentum spaces of spin one and three. If we consider both spin 1 and 1 2 states, then the same method will lead to the Lie-super algebra osp(1,2). Also, the quantum generalization of the method is discussed on the basis of the quantum group suq(2). * Paper...

On some nonlinear extensions of the angular momentum algebra

Deformations of the Lie algebras so(4), so(3,1), and e(3) that leave their so(3) subalgebra undeformed and preserve their coset structure are considered. It is shown that such deformed algebras are associative for any choice of the deformation parameters. Their Casimir operators are obtained and some of their unitary irreducible representations are constructed. For vanishing deformation, the la...

A representation of angular momentum (SU (2)) algebra

This paper seeks to construct a representation of the algebra of angular momentum (SU(2) algebra) in terms of the operator relations corresponding to Gentile statistics in which one quantum state can be occupied by n particles. First, we present an operator realization of Gentile statistics. Then, we propose a representation of angular momenta. The result shows that there exist certain underlyi...

Angular Momentum