The q-Euclidean algebra $U_q(e^N)$ and the corresponding q-Euclidean lattice

Abstract

We review the Euclidean Hopf algebra $U_q(e^N)$ dual of $Fun(\rn_q^N\lcross SO_{q^{-1}}(N))$ and describe its fundamental Hilbert space representations \cite{fioeu}, which turn out to be rather simple "lattice-regularized" versions of the classical ones, in the sense that the spectra of squared momentum components are discrete and the corresponding eigenfunctions normalizable.These representations can be regarded as describing a quantum system consisting of one free particle on the quantum Euclidean space. A suitable notion of classical limit is introduced, so that we recover the classical continuous spectra and generalized (non-normalizable) eigenfunctions in that limit.

19pages, latex. transmission error corrected

References in corpus (2)

• The Euclidean Hopf algebra $U_q(e^N)$ and its fundamental Hilbert space representations
• Realization of $U_q(so(N))$ within the differntial algebra on ${\mathbf{R}}_q^N$

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