CLASSICAL MECHANICS AS QUANTUM-MECHANICS WITH INFINITESIMAL-H

We define the classical limit of quantum theory in the mathematical fr amework of nonstandard analysis, choosing h as an infinitesimal number . Up to corrections of infinitesimally small norm, bounded observables which change continuously on the standard (non-infinitesimal) phase s pace scale, are identified with functions on phase space. We discuss t he convergence of commutators to Poisson brackets, and the quantum tim e evolution to the classical one. These results are also shown for the classical limit of spin systems, by choosing the spin as an infinite half-integer.