E_A \quad \forall f \in C^\infty(D{\mathcal{M}})
\\
{\nabla\hspace{-3mm}{/}}h &=& ({\nabla\hspace{-3mm}{/}}h)_B E^B =
\eta^{\alpha\beta}(\nabla_\beta h_C)\gamma_{\alpha\,\,\,\, B}^{\,\,\, C} E^B
\quad \forall h \in C^\infty(D^*{\mathcal{M}}) \, .\end{aligned}$$ The spinor field $f\in C^\infty(D{\mathcal{M}})$ is said to satisfy the Dirac equation if $(-i{\nabla\hspace{-3mm}{/}}+\mu)f=0$ where the constant $\mu\geq 0$ is interpreted as the mass of the field. Similarly, the cospinor field $h \in C^\infty(D^*{\mathcal{M}})$ is said to satisfy the Dirac equation if $(i{\nabla\hspace{-3mm}{/}}+\mu)h=0$.

Even though the Dirac operator is not normally hyperbolic it is possible to find unique advanced and retarded fundamental solutions on arbitrary globally hyperbolic spacetimes. The key element in this analysis is the Lichnérowicz identity, $$\label{lich}
P = (-i{\nabla\hspace{-3mm}{/}}+\mu)(i{\nabla\hspace{-3mm}{/}}+\mu)$$ where $P=\nabla^2+R/4+\mu^2$ is the so-called supersymmetrically coupled Klein-Gordon operator for spinors, which relates Dirac operators to normally hyperbolic ones. The $R$ featuring in (\[lich\]) is the Ricci scalar. It is known that there exist unique advanced $E^-_P$ and retarded $E^+_P$ fundamental solutions to any normally hyperbolic operator $P$ on globally hyperbolic spacetimes. Hence, for the spinor field, one has the following fundamental solutions: $S^\pm_\textrm{sp}=(i{\nabla\hspace{-3mm}{/}}+\mu)E^\pm_P$. To be explicit, $S^\pm_\textrm{sp}$ are continuous operators $S^\pm_\mathrm{sp}: C^\infty_0(D{\mathcal{M}})\mapsto C^\infty(D{\mathcal{M}})$ such that $$(-i{\nabla\hspace{-3mm}{/}}+\mu)S^\pm_\mathrm{sp} f =
S^\pm_\mathrm{sp}(-i{\nabla\hspace{-3mm}{/}}+\mu)f =f$$ satisfying ${\textrm{supp }}(S^\pm_\mathrm{sp} f)\subset J^\pm ({\textrm{supp }}f)$. Clearly, there is a similar construction 