2020 Impact factor 4.590
Particles and Fields
Eur. Phys. J. C 16, 169-180
DOI 10.1007/s100520000427

Structure of the three-dimensional quantum euclidean space

B.L. Cerchiai1,2 - J.Madore2,3 - S. Schraml1,2 - J. Wess1,2

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

Received: 13 April 2000 / Published online: 18 May 2000 - © Springer-Verlag 2000

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.

Copyright Società Italiana di Fisica, Springer-Verlag 2000