Canonical commutation relation preserving maps

We study maps preserving the Heisenberg commutation relation ab-ba=1. We find a one-parameter deformation of the standard realization of the above algebra in terms of a coordinate and its dual derivative. It involves a non-local 'coordinate' operator while the dual 'derivative' is just the Jackson finite-difference operator. Substitution of this realization into any differential operator involving x and d/dx results in an isospectral deformation of a continuous differential operator into a finite-difference one. We extend our results to the deformed Heisenberg algebra ab-qba=1. As an example of potential applications, various deformations of the Hahn polynomials are briefly discussed. (author)