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Canonical Commutation Relation Preserving Maps | | C. Chryssomalakos
; A. Turbiner
; | | Date: |
3 Apr 2001 | | Subject: | Mathematical Physics; Numerical Analysis; Quantum Algebra | math-ph hep-th math.MP math.NA math.QA | | Abstract: | 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 $frac{d}{dx}$, results in an {em 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. | | Source: | arXiv, math-ph/0104004 | | Services: | Forum | Review | PDF | Favorites | |
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