Representation theory and Wigner-Racah algebra of the SU(2) group in a noncanonical basis
Abstract
Description
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.
To be presented at ICSSUR'05 (9th International Conference on Squeezed States and Uncertainty Relations, France, 2-6 May 2005). Dedicated to Professor Josef Paldus on the occasion of his 70th birthday. To be published in Collection of Czechoslovak Chemical Communications
To be presented at ICSSUR'05 (9th International Conference on Squeezed States and Uncertainty Relations, France, 2-6 May 2005). Dedicated to Professor Josef Paldus on the occasion of his 70th birthday. To be published in Collection of Czechoslovak Chemical Communications