Structure of the three-dimensional quantum euclidean space

B.L. Cerchiai; J.Madore; S. Schraml; J. Wess

doi:doi:10.1007/s100520050013

EPJ

Structure of the three-dimensional quantum euclidean space

B.L. Cerchiai^1,2 - J.Madore^2,3 - S. Schraml^1,2 - J. Wess^1,2

¹ Sektion Physik, Universität München, Theresienstrasse 37, 80333 München, Germany
² Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München, Germany
³ Laboratoire de Physique Théorique Université de Paris-Sud, Bâtiment 211, 91405 Orsay, France

Abstract
As an example of a noncommutative space we discuss the quantum 3-dimensional Euclidean space $\b R^3_q$ together with its symmetry structure in great detail. The algebraic structure and the representation theory are clarified and discrete spectra for the coordinates are found. The q-deformed Legendre functions play a special role. A completeness relation is derived for these functions.