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Covariant (hh′)-deformed bosonic and fermionic algebras as contraction limits of q-deformed ones

par Quesne, Christiane
Référence International journal of theoretical physics, 38, 7, page (1905-1923)
Publication Publié, 1999-07

Article révisé par les pairs

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Résumé :

GLh(n) × GLh′(m)-covariant (hh′)-bosonic [or (hh′)-fermionic] algebras Script A signhh′±(n, m) are built in terms of the corresponding Rh and Rh′,-matrices by contracting the GLq(n) × GLq±i(m)-covariant q-bosonic (or q-fermionic) algebras Script A sign(α)q±(n, m), α = 1, 2. When using a basis of Script A sign(α)q±(n, m) wherein the annihilation operators are contragredient to the creation ones, this contraction procedure can be carried out for any n, m values. When employing instead a basis wherein the annihilation operators, like the creation ones, are irreducible tensor operators with respect to the dual quantum algebra Uq(gl(n)) ⊗ Uq±i (gl(m)), a contraction limit only exists for n, m ∈ [ 1, 2, 4, 6, . . .]. For n = 2, m = 1, and n = m = 2, the resulting relations can be expressed in terms of coupled (anti)commutators (as in the classical case), by using Uh(sl(2)) [instead of s1(2)] Clebsch-Gordan coefficients. Some Uh(sl(2)) rank-1/2 irreducible tensor operators recently constructed by Aizawa are shown to provide a realization of Script A signh±(2, 1).