Collection of Czechoslovak Chemical Communications - digital archive 

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 generators J_- and J₊ of the SU(2) group, with J₊ = J_-^† = HU_r where H is Hermitean and U_r unitary, and (ii) an alternative to the {J²,J_z} quantization scheme, viz., the {J²,U_r} 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,U_r} scheme are given. In particular, some properties of the coupling and recoupling coefficients as well as the Wigner-Eckart theorem in the {J²,U_r} scheme are examined in great detail.

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

References: 105 live references.