2012/04/30 by A. M. Gavrilik, A. M. GAVRILIK, I. I. Kachurik +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Commutator #Deformation (meteorology) #Operator (biology) #Operator algebra #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1142/s0217732312501143
published as Mod. Phys. Lett. A, Vol. 27, No. 21 (2012) 1250114 · 12 pages; v2: minor changes and few references added, accepted in Mod.Phys.Lett.A
arxiv created 2012/06/07 · openalex publication_date 2012/06/28 · arxiv updated 2012/07/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A three-parametric two-sided deformation of Heisenberg algebra (HA), with p, q-deformed commutator in the L.H.S. of basic defining relation and certain deformation of its R.H.S., is introduced and studied. The third deformation parameter μ appears in an extra term in the R.H.S. as pre-factor of Hamiltonian. For this deformation of HA we find novel properties. Namely, we prove it is possible to realize this (p, q, μ)-deformed HA by means of some deformed oscillator algebra. Also, we find the unusual property that the deforming factor μ in the considered deformed HA inevitably depends explicitly on particle number operator N. Such a novel N-dependence is special for the two-sided deformation of HA treated jointly with its deformed oscillator realizations.