On Dirac equations on phase spaces

In this paper, we consider Dirac equations on relativistic phase spaces [Formula: see text], where [Formula: see text] is Minkowski space with [Formula: see text]. We use the geometric quantization approach in which the wave functions are polarized sections of a complex line bundle [Formula: see text] over [Formula: see text]. The covariant derivatives with connection [Formula: see text] in this bundle define canonical commutation relations. Fermions are charged with respect to the field [Formula: see text], so lifting the Dirac equations from space-time [Formula: see text] to phase space [Formula: see text] results in their solutions being localized in the space [Formula: see text] or in space-time [Formula: see text]. We describe the explicit form of these solutions.