Towards the canonical tensor operators of {ital u}{sub {ital q}}(3). I. The maximal null space case
- Institute of Theoretical Physics and Astronomy, A. Gostauto 12, Vilnius 2600 (Lithuania)
Generalizing the SU(3) canonical tensor operator concept (Biedenharn and Louck) to the quantum algebra {ital u}{sub {ital q}}(3), the Wigner{endash}Clebsch{endash}Gordan coefficients of {ital u}{sub {ital q}}(3) with repeating irreducible representations are considered. Extremal projectors of the quantum algebra {ital u}{sub {ital q}}(3) in terms of the ordered generator polynomials are used for evaluation of the bilinear combinations of the {ital u}{sub {ital q}}(3) canonical isoscalar factors. Explicit expressions of the {ital u}{sub {ital q}}(3) isofactors, corresponding to the maximal null space case of the {ital u}{sub {ital q}}(3) unit canonical tensor operators, and their normalization factors (denominator functions) are presented. The transposition and conjugation phase factors for the SU(3) and {ital u}{sub {ital q}}(3) canonical isofactors are correlated with phases and zeros of boundary isofactors. Invariance of the canonical isofactors (or absence of such invariance) under interchange of the tensor operator and the initial or final state parameters is correlated with the existence and invariance (or numerical degeneracy) of the usual splitting (distinctive) conditions. Some oversights of previous publications are disclosed. {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 388206
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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