Analysis on the 2-Dim Quantum Poincare Group at Roots of Unity

Authors : Haji AHMEDOV

Pages : 175-192

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :2--Dim quantum Poincar\`e Group Eqinsert ignore into journalissuearticles values(1,1); at roots of unity, its dual Uqinsert ignore into journalissuearticles values(einsert ignore into journalissuearticles values(1,1);); and some of its homogeneous spaces are introduced. Invariant integrals on Eqinsert ignore into journalissuearticles values(1,1); and its invariant discrete subgroup Einsert ignore into journalissuearticles values(1,1\mid p); are constructed. *--Representations of the quantum algebra Uqinsert ignore into journalissuearticles values(einsert ignore into journalissuearticles values(1,1);); constructed in the homogeneous space SOinsert ignore into journalissuearticles values(1,1\mid p); are integrated to the pseudo--unitary representations of Eqinsert ignore into journalissuearticles values(1,1); by means of the universal T--matrix. Uqinsert ignore into journalissuearticles values(einsert ignore into journalissuearticles values(1,1);); is realized on the quantum plane Eqinsert ignore into journalissuearticles values(1,1); and the eigenfunctions of the complete set of observables are obtained in the angular momentum and momentum basis. The matrix elements of the pseudo--unitary irreducible representations are given in terms of the cut off q--exponential and q--Bessel functions whose properties we also investigate.
Keywords : Turk J Phys, 24, 2000, 175 192 Turk J Phys, vol 24, iss 3