Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-09-09
Commun.Math.Phys. 175 (1996) 161-176
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, plain tex, revised version with added material
Scientific paper
10.1007/BF02101628
After a preliminary review of the definition and the general properties of the homogeneous spaces of quantum groups, the quantum hyperboloid qH and the quantum plane qP are determined as homogeneous spaces of Fq(E(2)). The canonical action of Eq(2) is used to define a natural q-analog of the free Schro"dinger equation, that is studied in the momentum and angular momentum bases. In the first case the eigenfunctions are factorized in terms of products of two q-exponentials. In the second case we determine the eigenstates of the unitary representation, which, in the qP case, are given in terms of Hahn-Exton functions. Introducing the universal T-matrix for Eq(2) we prove that the Hahn-Exton as well as Jackson q-Bessel functions are also obtained as matrix elements of T, thus giving the correct extension to quantum groups of well known methods in harmonic analysis.
Bonechi Francesco
Ciccoli Nicola
Giachetti Riccardo
Sorace Emanuele
Tarlini Marco
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