SU(2) × SU(2) × U(1) basis for symmetric SO(6) representations : matrix elements of the generators

R. Piepenbring (1) , B. Silvestre-Brac (1) , Z. Szymanski (1)

1 LPSC - Laboratoire de Physique Subatomique et de Cosmologie

Matrix elements of the group generators for the symmetric irreducible representations of SO(6) are explicitly calculated in a closed form employing the decomposition chain SO(6) ⊃ SU(2) x SU(2) x U(1) (which is different from the well known Wigner supermultiplet scheme). The relation to the Gel'fand Tsetlin method using SO(6) ⊃ SO(5) ⊃ ... ⊃ SO(2) is indicated. An example of a physical application is given.

Mots clés: matrix algebra; SO groups; SU/sub 2/ theory

Domaines: Articles anciens; Physique Quantique [quant-ph]

R. Piepenbring, B. Silvestre-Brac, Z. Szymanski. SU(2) × SU(2) × U(1) basis for symmetric SO(6) representations : matrix elements of the generators. Journal de Physique, 1987, 48 (4), pp.577-584. ⟨10.1051/jphys:01987004804057700⟩. ⟨jpa-00210472⟩