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 whic h result in different (commutative and noncommutative) algebras of ''c lassical'' observables are derived. In particular, this gives the q-de formed Poisson brackets in terms of variables on the quantum planes. W e consider a Hamiltonian constructed with a special combination of ope rators (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.