  Classical mechanics, in the operatorial formulation of Koopman and von
Neumann, can be written also in a functional form. In this form two Grassmann
partners of time make their natural appearance extending in this manner time to
a three dimensional supermanifold. Quantization is then achieved by a process
of dimensional reduction of this supermanifold. We prove that this procedure is
equivalent to the well-known method of geometric quantization.
