On Dirac equations on phase spaces

We consider Dirac equations on relativistic phase spaces $T^*{\mathbb R}^{p-1,1}$, where ${\mathbb R}^{p-1,1}$ is Minkowski space with $p=2,4$. We use the geometric quantization approach in which the wave functions are polarized sections of a complex line bundle $L_{\sf{v}}$ over $T^*{\mathbb R}^{p-1,1}$. The covariant derivatives with connection $A_{\sf{vac}}$ in this bundle define canonical commutation relations. Fermions are charged with respect to the field $A_{\sf{vac}}$, so lifting the Dirac equations from space-time ${\mathbb R}^{p-1,1}$ to phase space $T^*{\mathbb R}^{p-1,1}$ results in their solutions being localized in the space ${\mathbb R}^{p-1}$ or in space-time ${\mathbb R}^{p-1,1}$. We describe the explicit form of these solutions.