Dergiler / Turkish Journal of Physics / 2000 / Cilt: 24 - Sayı: 3
Analysis on the 2-Dim Quantum Poincare Group at Roots of Unity
- Sayfa
- 175–191
- DOI
- —
Özet
2--Dim quantum Poincar\'e Group Eq(1,1) at roots of unity, its dual Uq(e(1,1)) and some of its homogeneous spaces are introduced. Invariant integrals on Eq(1,1) and its invariant discrete subgroup E(1,1\mid p) are constructed. *--Representations of the quantum algebra Uq(e(1,1)) constructed in the homogeneous space SO(1,1\mid p) are integrated to the pseudo--unitary representations of Eq(1,1) by means of the universal T--matrix. Uq(e(1,1)) is realized on the quantum plane Eq(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.
Abstract
2--Dim quantum Poincar\'e Group Eq(1,1) at roots of unity, its dual Uq(e(1,1)) and some of its homogeneous spaces are introduced. Invariant integrals on Eq(1,1) and its invariant discrete subgroup E(1,1\mid p) are constructed. *--Representations of the quantum algebra Uq(e(1,1)) constructed in the homogeneous space SO(1,1\mid p) are integrated to the pseudo--unitary representations of Eq(1,1) by means of the universal T--matrix. Uq(e(1,1)) is realized on the quantum plane Eq(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.