Classical and quantum mechanics via supermetrics in time
  Koopman-von Neumann in the 30's gave an operatorial formululation of
Classical Mechanics. It was shown later on that this formulation could also be
written in a path-integral form. We will label this functional approach as CPI
(for classical path-integral) to distinguish it from the quantum mechanical
one, which we will indicate with QPI. In the CPI two Grassmannian partners of
time make their natural appearance and in this manner time becomes something
like a three dimensional supermanifold. Next we introduce a metric in this
supermanifold and show that a particular choice of the supermetric reproduces
the CPI while a different one gives the QPI.
