Pré-Publication, Document De Travail Année : 2017

Partitions of Wigner 3-j or Super 3-j symbols induced by Regge symmetry : accurate description

Résumé

We show that Regge transformations induce five partitions on (3-j) symbols of su(2) , namely Sp(0), Sp(1), Sp(2), Sp(4), Sp(5), with an empty set Sp(3) = ∅. The super-algebra osp(1|2) admits three kinds of super-symbols (3-j) Salpha, (3-j) Sbeta ,(3-j) Sgamma , whose alpha, beta, gamma parities are fixed by the values of 2(j ± m). We find also five partitions for (3-j) Salpha, (3-j) Sgamma symbols of osp(1|2), but they reduce to Sp(0), Sp(1) for a (3-j) Sbeta . Unexpectedly this latter and its ‘Regge-transformed’ may be opposite in sign. A formula fully similar to that of a (3-j) is derived for the (3-j) S . Some forbidden (3-j) Sbeta requires an analytic prolongation, consistent with Regge beta-partitions, which enables us to establish a complete (3-j) S table.

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hal-01162475 , version 1 (10-06-2015)

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Lionel Bréhamet. Partitions of Wigner 3-j or Super 3-j symbols induced by Regge symmetry : accurate description. 2017. ⟨hal-01162475⟩

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