2000/09/28 by Alfredo Iorio, Iorio, Alfredo, Giuseppe Vitiello +1
Chemistry · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0009036
7 pages, LaTeX. Invited lecture at the Third International Workshop on Thermal Field Theories, Banff, Canada, August 1993
arxiv created 2000/09/28 · openalex publication_date 2000/09/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the canonical quantization of the damped harmonic oscillator by resorting to the realization of the q-deformation of the Weyl-Heisenberg algebra (q-WH) in terms of finite difference operators. We relate the damped oscillator hamiltonian to the q-WH algebra and to the squeezing generator of coherent states theory. We also show that the q-WH algebra is the natural candidate to study thermal field theory. The well known splitting, in the infinite volume limit, of the space of physical states into unitarily inequivalent representations of the canonical commutation relations is briefly commented upon in relation with the von Neumann theorem in quantum mechanics and with q-WH algebra.