2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168897In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the ordinary pointwise product of functions, whereas geometric quantization is a prescription for the construction of a Hilbert space and a few quantum operators, starting from a symplectic manifold. We determine under which conditions it is possible to define a representation of the deformed algebra on this Hilbert space, thereby to extend the small class of quantizable observables in geometric quantization to all smooth functions, as well as to give a natural representation of the algebra. In particular we look at the special cases of a cotangent bundle and a Kähler manifold.20 pagesMathematical Physicstext