Representations of the Weyl group and Wigner functions for SU(3)

Details Representations of the Weyl group and Wigner functions for SU(3) Representations of the Weyl group and Wigner functions for SU(3)

1998-11-13

arxiv.org/abs/math-ph/9811012v2

Physics

Mathematical Physics

: RevTex file, 11 pages with 2 figures

Scientific paper

10.1063/1.532911

Bases for SU(3) irreps are constructed on a space of three-particle tensor products of two-dimensional harmonic oscillator wave functions. The Weyl group is represented as the symmetric group of permutations of the particle coordinates of these space. Wigner functions for SU(3) are expressed as products of SU(2) Wigner functions and matrix elements of Weyl transformations. The constructions make explicit use of dual reductive pairs which are shown to be particularly relevant to problems in optics and quantum interferometry.

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