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Hecht, K. T.; Biedenharn, L. C.

Vector coherent state constructions of \(U(3)\) symmetric tensors and their \(SU(3)\supset SU(2)\times U(1)\) Wigner coefficients. (English) Zbl 0741.22017

J. Math. Phys. 31, No. 12, 2781-2796 (1990).
Vector coherent states (VCS) proved to be a useful tool in studying matrix representations of \(U(n)\) (large \(n\)) in a more explicit manner. The article gives the Bargmann space realization of the set of totally symmetric \(U(3)\) tensor operators using the VCS approach. In effect, each tensor operator is factored into an intrinsic operator acting on \(U(1)\)- extremal states and a Bargmann space operator changing the \(U(1)\) weights. The reduced matrix elements (with respect to the subgroup \(SU(2)\times U(1))\) of the intrinsic part are evaluated explicitly and reduced Wigner coefficients are given in this new representation. The results are then compared to previous special findings of Le Blanc- Biedenharn. The authors feel that they have obtained the simplest expressions from the point of view of actual computation.
Reviewer: G.Roepstorff (Aachen)

Cited in 4 Documents

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations

Keywords:

vector coherent states; matrix representations; tensor operators; Bargmann space operator; weights; reduced matrix elements; reduced Wigner coefficients
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