Turkish Journal of Physics
DOI
-
Abstract
2--Dim quantum Poincar\'e Group $E_q(1,1)$ at roots of unity, its dual $U_q(e(1,1))$ and some of its homogeneous spaces are introduced. Invariant integrals on $E_q(1,1)$ and its invariant discrete subgroup $E(1,1\mid p)$ are constructed. $*$--Representations of the quantum algebra $U_q(e(1,1))$ constructed in the homogeneous space $SO(1,1\mid p)$ are integrated to the pseudo--unitary representations of $E_q(1,1)$ by means of the universal $T$--matrix. $U_q(e(1,1))$ is realized on the quantum plane $E_q^{(1,1)}$ 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.
First Page
175
Last Page
192
Recommended Citation
AHMEDOV, HAJI (2000) "Analysis on the 2-Dim Quantum Poincare Group at Roots of Unity," Turkish Journal of Physics: Vol. 24: No. 3, Article 2. Available at: https://journals.tubitak.gov.tr/physics/vol24/iss3/2
