1993/10/20 by Celeghini, E. Celeghini, S. Demartino +7 · 62 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebra over a field #Coherent states #Coherent states in mathematical physics #Creation and annihilation operators #Fock space #Lattice (music) #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Second quantization #Squeezed coherent state #Theoretical physics #hep-th
paper · pdf · doi:10.1006/aphy.1995.1055
published in Annals of Physics 241(1), 50-67 (Elsevier BV) · 22 pages, TEX file, DFF188/9/93 Firenze
arxiv created 1993/10/20 · openalex publication_date 1995/07/01 · arxiv updated 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg (q-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the q--WH algebra in terms of finite difference operators. The physical relevance of our study relies on the fact that coherent states (CS) are indeed formulated in the space of entire analytic functions where they can be rigorously expressed in terms of theta functions on the von Neumann lattice. The rôle played by the finite difference operators and the relevance of the lattice structure in the completeness of the CS system suggest that the q--deformation of the WH algebra is an essential tool in the physics of discretized (periodic) systems. In this latter context we define a quantum mechanics formalism for lattice systems.