Canonical Commutation Relation Preserving Maps

Details Canonical Commutation Relation Preserving Maps Canonical Commutation Relation Preserving Maps

2001-04-02

arxiv.org/abs/math-ph/0104004v2

Physics

Mathematical Physics

11 pages. To appear in J. Phys. A., Special Issue on Difference Equations Revised version: an important note, communicated to

Scientific paper

10.1088/0305-4470/34/48/312

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.

Affiliated with

Also associated with

No associations

Rating

Canonical Commutation Relation Preserving Maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Canonical Commutation Relation Preserving Maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Canonical Commutation Relation Preserving Maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-173645