2005/10/31 by Gerald A. Goldin, Gerald A Goldin, Sarben Sarkar
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #hep-th
paper · pdf · doi:10.1088/0305-4470/39/11/012
published as J.Phys. A39 (2006) 2757-2772 · 10 pages REVTex, no figures
arxiv created 2006/01/31 · openalex publication_date 2006/03/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We explore some explicit representations of a certain stable deformed algebra of quantum mechanics, considered by R Vilela Mendes, having a fundamental length scale. The relation of the irreducible representations of the deformed algebra to those of the (limiting) Heisenberg algebra is discussed, and we construct the generalized harmonic oscillator Hamiltonian in this framework. To obtain local currents for this algebra, we extend the usual nonrelativistic local current algebra of vector fields and the corresponding group of diffeomorphisms, modelling the quantum configuration space as a commutative spatial manifold with one additional dimension.