Collect. Czech. Chem. Commun. 2005, 70, 771-796

Representation Theory and Wigner-Racah Algebra of the SU(2) Group in a Noncanonical Basis

Maurice R. Kibler

Institut de Physique Nucléaire de Lyon, IN2P3-CNRS et Université Claude Bernard Lyon 1, 43 bd du 11 novembre 1918, 69622 Villeurbanne Cedex, France


The Lie algebra su(2) of the classical group SU(2) is built from two commuting quon algebras for which the deformation parameter is a common root of unity. This construction leads to (i) a not very well-known polar decomposition of the generators J- and J+ of the SU(2) group, with J+ = J- = HUr where H is Hermitean and Ur unitary, and (ii) an alternative to the {J2,Jz} quantization scheme, viz., the {J2,Ur} quantization scheme. The representation theory of the SU(2) group can be developed in this nonstandard scheme. The key ideas for developing the Wigner-Racah algebra of the SU(2) group in the {J2,Ur} scheme are given. In particular, some properties of the coupling and recoupling coefficients as well as the Wigner-Eckart theorem in the {J2,Ur} scheme are examined in great detail.

Keywords: Wigner-Eckart theorem; Hermitean; Oscillator algebras; Quantum mechanics; Quantum chemistry.

References: 105 live references.