The geometry of a q-deformed phase space
B.L. Cerchiai1,2 - R. Hinterding 1,2 - J. Madore2,3 - J. Wess 1,2
1 Sektion Physik, Ludwig-Maximilian Universität, Theresienstraße 37,
D-80333 München, Germany
2 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, D-80805 München, Germany
3 Laboratoire de Physique Théorique et Hautes Energies, Université de Paris-Sud, Bâtiment 211, F-91405 Orsay, France
Received: 26 November 1998 / Published online: 27 April 1999
The geometry of the q-deformed line is studied. A real differential calculus is introduced and the associated algebra of forms represented on a Hilbert space. It is found that there is a natural metric with an associated linear connection which is of zero curvature. The metric, which is formally defined in terms of differential forms, is in this simple case identifiable as an observable.