Quasi-classical limit in q-deformed systems, non-commutativity and the q-path integral

Different analogs of the quasi-classical limit for a q-oscillator which result in different (commutative and noncommutative) 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 a Hamiltonian constructed with a special combination of operators (the analog of even operators in Grassmann algebra) and discuss g-path integrals constructed with the help of contracted ''classical'' algebras. (C) 1997 Elsevier Science B.V.