Abstract
The covariant differential calculus on the quantum vector space CNq leads to q deformations of the canonical commutation relations and of the Weyl algebra. If the deformation parameter q is of modulus one, integrable (‘‘well-behaved’’) representations of this twisted canonical commutation relations by self-adjoint operators on a Hilbert space are defined and studied. All faithful irreducible integrable representations of the real q-Weyl algebra are classified up to unitary equivalence.
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