The Poisson bracket for \(q\)-deformed systems. (English) Zbl 0771.58018
Summary: It is shown that the quantum system of \(q\)-deformed oscillators with the \(U_ q(n)\) group symmetry can be obtained by the canonical quantization of a classical system with a modified Poisson bracket. The modification of the Poisson bracket is connected with a noncanonical transformation of phase space variables. In this approach, the deformation parameter turns out to be a function of the Planck constant and some dimensional parameters characterizing the classical system.
MSC:
37J99 | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |
81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
53D50 | Geometric quantization |