Quantization and Classicization: from Jordan-lie Algebras of Observables to Gauge Elds

A uniied approach to classical and quantum mechanics is presented , based on the use of Jordan-Lie algebras. Examples of such algebras of physical observables are constructed, which describe a particle moving on a certain class of curved spaces. In the spirit of the algebraic theory of superselection sectors, irreducible representations of the quantum algebras are identiied with possible quantizations of the system in question. An analogous procedure for classical observables leads to a classical analogue of a quantization, called a `classicization'. In either case, the various sectors correspond to the particle having acquired an internal charge, which naturally couples to an induced Yang-Mills eld.