1997/03/02 by A. Z. Górski, Andrzej Z. Gorski, Jacek Szmigielski · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #gr-qc #hep-th #math.QA #q-alg #quant-ph
paper · pdf · doi:10.1063/1.532322
published as J.Math.Phys. 39 (1998) 545-568 · 32 pages, plain TeX
arxiv created 1997/03/02 · openalex publication_date 1998/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dedicated to the memory of Gerda Dorfmeister. Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider D and X to be self-adjoint and skew self-adjoint or whether they have to be viewed as creation and annihilation operators. The first class, generalizing the central difference scheme, is shown to give unitary equivalent representations. For the second case we construct a large class of examples, generalizing previously known difference operator realizations of [D, X]=Id.