Quasiclassical Limit in q-Deformed Systems, Noncommutativity and the q-Path Integral

Abstract

Different analogs of quasiclassical limit for a q-oscillator which result in different (commutative and non-commutative) algebras of ``classical'' observables are derived. In particular, this gives the q-deformed Poisson brackets in terms of variables on the quantum planes. We consider the Hamiltonian made of special combination of operators (the analog of even operators in Grassmann algebra) and discuss q-path integrals constructed with the help of contracted ``classical'' algebras.

19 pages, Latex

References in corpus (2)

• Discrete Heisenberg-Weyl Group and Modular Group
• Path Integrals with Generalized Grassmann Variables

Cited by in corpus (5)

• Exact methods in analysis of nonequilibrium dynamics of integrable models: application to the study of correlation functions in nonequilibrium 1D Bose gas
• Classical and quantum q-deformed physical systems
• Revisiting the dynamic of Q-deformed logistic maps
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish
• Distortion of the Poisson Bracket by the Noncommutative Planck Constants