Abstract
The explicit algebraic construction of irreducible tensor operators with definite shift properties is central to the solution of all problems involving symmetries in physics, the compact Lie groups being of particular interest. The pioneering work of Larry Biedenharn in the construction of a canonical tensor calculus for the unitary groups1−6 is well known. By giving a canonical (author-independent) prescription for the SU(3) tensors, in particular, the Biedenharn-Louck construction gives an elegant resolution to the “multiplicity problem” which plagues all higher rank Lie algebras. Although the problem was resolved for SU(3), m principle, as early as the 1960’s, the algebraic labor of giving a viable explicit construction of such tensors presented a formidable task at that time, as illustrated by the construction of all 27-plet SU(3) tensor operators by Castilho Alcaras et al.7
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References
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Hecht, K.T. (1993). Vector Coherent State Constructions of U(3) Canonical Shift Tensors of Biedenharn-Louck Type. In: Gruber, B. (eds) Symmetries in Science VI. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1219-0_26
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DOI: https://doi.org/10.1007/978-1-4899-1219-0_26
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