DOI 10.1007/s100520000472
Realization of the three-dimensional quantum Euclidean space by differential operators
S. Schraml - J. Wess
Max-Planck-Institut für Physik,
Föhringer Ring 6, 80805 München, Germany
-
Sektion Physik, Universität München,
Theresienstrasse 37, 80333 München, Germany
Received: 27 June 2000 / Published online: 9 August 2000 - © Springer-Verlag 2000
Abstract
The three-dimensional quantum Euclidean space is an example of a non-commutative space
that is obtained from Euclidean space by q-deformation. Simultaneously, angular
momentum is deformed to soq(3), it acts on the q-Euclidean space that becomes a
soq(3)-module algebra this way. In this paper it is shown, that this algebra can be
realized by differential operators acting on
functions on
.
On a factorspace of
a scalar product can
be defined that leads to a Hilbert space, such that the action of the
differential operators is defined on a dense set in this Hilbert space and algebraically
self-adjoint becomes self-adjoint for the linear operator in the Hilbert space. The
self-adjoint coordinates have discrete eigenvalues, the spectrum can be considered as a
q-lattice.
Copyright Società Italiana di Fisica, Springer-Verlag 2000