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- W2009404585 abstract "Starting from a primitive 6-j symbol for SO (2l+1) in which four elementary spinor irreducible representations (irreps) (. . .) appear, and using the properties of the Kronecker products of partially stretched irreps, the authors develop a bootstrap procedure, based on a generalisation of the Biedenharn-Elliott sum rule, for calculating other 6-j and 9-j symbols for SO(2l+1). Several of their formulae can be expressed in terms of SO(3) 3-j symbols and rotation matrices d jmn( pi ). An explanation for this is found by using the complementary groups whose generators involve the spin S and quasispin Q of electrons in an atomic l shell. The relation between the two kinds of coupling, that of the irreps of SO(2l+1) and that of the SO(3) angular momenta, is particularly fruitful if the quasiparticle description is employed for the electrons. A further bootstrap leads to a formula for an SO(2l+1) 6-j symbol whose six irreps are all of the type (11 . . . 10 . . . 0), and this is shown to be consistent with a formula for an Sp(2n) 6-j symbol if one replaces 2n by the negative dimensions -2l-1." @default.
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- W2009404585 date "1990-02-21" @default.
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- W2009404585 title "6-j symbols for SO(2l+1) and a structural analysis in terms of atomic quasiparticles" @default.
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- W2009404585 doi "https://doi.org/10.1088/0305-4470/23/4/011" @default.
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