Tensor operator realisations of the classical Lie Algebras and non-trivial zeros of the 6j-symbol
1984; Springer Science+Business Media; Linguagem: Inglês
10.1007/bfb0016128
ISSN1616-6361
AutoresJ. Van der Jeugt, H. De Meyer, Greet Van den Berghe, Philippe De Wilde,
Tópico(s)Mathematics and Applications
ResumoThe existence of an infinity of zeros of Racah's 6j-symbol which are non trivial in the sense that they do not result from triangle condition violation has been discussed recently by Biedenharn and Louck I). In their book the tonic is illustrated by means of an extensive table containing more than 1400 structural zeros. Clearly, in remaining within the framework of the SO(3) Lie algebra A I in which the 6j-symbol naturally arises, the structural zeros coincide with the zeros of a function depending on six non-negative integer or half-odd integer variables of which the domain of definition is restricted to all entries which satisfy the triangle conditions. As an example, it is easy to deduce from Racah's well-known algebraic formula 2) of the 6j-symbol that the one-parameter family of 6j-c°efficientsI3a-4a aa 2a-2a-~ , where 2a~+ and a~2, yields an infinity of such
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