  The Dirac's formalism for constrained systems is applied to the analysis of
time-dependent Hamiltonians in the extended phase space. We show that the Lewis
invariant is a reparametrization invariant and we calculate the Feynman
propagator using the extended phase description. We show that the quantum phase
of the Feynman propagator is given by the boundary term of the canonical
transformation of the extended phase space.
