Representation Functions d^j_<mk>of U[sl_q(2)] as Wave Functions of'Quantum Symmetric Tops'and Relationship to Braiding Matrices
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Quantum #-functions d',.., which constitute the (2781)-dimensional representalion matrix of the quantum group U(sl,(2)J, are investigated to specify them as wavefunctions of 'quantum symmetric tops' in the noncommutative space. It is shownthat the #-functions are solutions to the equation RT"T"'= T"' T"R, known in thequantum inverse scattering method, where R is the (27'-l-1)X(27"81) braidingmatrix of U(sl.(2)3. Quantum #-functions fulfill also Zamolodchikov-Zamolodchikov equation, which affords a new kind of braiding matrix that expresses scattering of a couple of quantum symmetric tops. Explicit forms of quantum #-functionsand several symmetry relations are obtained for them. Differential operations aregiven which describe space- and body-referred angular momentum operators of thequantum symmetric top. Description of quantum<7-functions in terms of creationand annihilation operators is also discussed.[quantum groups, matrix representations, quantum symmetric tops, quantum ]l Clebsch-Gordan coefficients, braiding matrices, creation and annihilation ll operatorsl
- 社団法人日本物理学会の論文
- 1990-12-15
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