Realization of the Three-dimensional Quantum Euclidean Space by Differential Operators

Simple item page
dc.creatorSchraml, Stefan
dc.creatorWess, Julius
dc.date2000-06-23
dc.date.accessioned2026-07-07T12:26:47Z
dc.date.available2026-07-07T12:26:47Z
dc.descriptionThe 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 $so_q(3)$, it acts on the $q$-Euclidean space that becomes a $so_q(3)$-module algebra this way. In this paper it is shown, that this algebra can be realized by differential operators acting on $C^{\infty}$ functions on $\mathbb{R}^3$. On a factorspace of $C^{\infty}(\mathbb{R}^3)$ 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.
dc.description13 pages, latex
dc.identifierhttps://arxiv.org/abs/math/0006179
dc.identifierhttp://arxiv.org/abs/math/0006179
dc.identifierEur.Phys.J.C17:353-358,2000
dc.identifierdoi:10.1007/s100520000472
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/214992
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subject81R50; 20G42
dc.titleRealization of the Three-dimensional Quantum Euclidean Space by Differential Operators
dc.typetext

Files

Collections

arXiv