On pairs of difference operators satisfying [D, X]=Id

DOI10.1063/1.532322zbMath0921.39006arXivhep-th/9703015OpenAlexW2089413849WikidataQ112166390 ScholiaQ112166390MaRDI QIDQ4212645

Andrzej Z. Górski, Jacek Szmigielski

Publication date: 15 September 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9703015

zbMATH Keywords

Heisenberg algebradiscrete derivativederivative operatorpairs of difference operators

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Difference operators (39A70) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Linear difference operators (47B39)

Related Items

One-dimensional quasi-exactly solvable Schrödinger equations, Analogue gravity, Representations of monomiality principle with Sheffer-type polynomials and boson normal ordering, Discrete phase space, relativistic quantum electrodynamics, and a non-singular Coulomb potential

Cites Work

• Strings in less than one dimension and the generalized KdV hierarchies
• Classification of certain pairs of operators (P,Q) satisfying \([P,Q=- iId\)]
• On the Heisenberg commutation relation. I
• Discreteness of area and volume in quantum gravity
• New quantum Poincaré algebra and \(\kappa\)-deformed field theory
• Canonical quantization of gravitating point particles in 2+1 dimensions
• Umbral calculus, discretization, and quantum mechanics on a lattice
• Transition from a continuous to a discrete space-time scheme