  For the description of space-time fermions, Dirac-K\"ahler fields
(inhomogeneous differential forms) provide an interesting alternative to the
Dirac spinor fields. In this paper we develop a similar concept within the
symplectic geometry of phase-spaces. Rather than on space-time, symplectic
Dirac-K\"ahler fields can be defined on the classical phase-space of any
Hamiltonian system. They are equivalent to an infinite family of metaplectic
spinor fields, i.e. spinors of Sp(2N), in the same way an ordinary
Dirac-K\"ahler field is equivalent to a (finite) mulitplet of Dirac spinors.
The results are interpreted in the framework of the gauge theory formulation of
quantum mechanics which was proposed recently. An intriguing analogy is found
between the lattice fermion problem (species doubling) and the problem of
quantization in general.
