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Representation theory and Wigner-Racah algebra of the SU(2) group in a noncanonical basis

M. R. Kibler
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Abstract

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 ladder generators of the SU(2) group, in terms of a unitary operator and a Hermitean operator, and (ii) a nonstandard quantization scheme, alternative to the usual quantization scheme correponding to the diagonalization of the Casimir of su(2) and of the z-generator. 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 nonstandard scheme are given. In particular, some properties of the coupling and recoupling coefficients as well as the Wigner-Eckart theorem in the nonstandard scheme are examined in great detail.

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M. R. Kibler. 2005-04-05. Representation theory and Wigner-Racah algebra of the SU(2) group in a noncanonical basis. https://arxiv.org/abs/quant-ph/0504025

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