  From a geometric point of view, massless spinors in $3+1$ dimensions are
composed of primary fields of weights $(\frac{1}{2},0)$ and $(0,\frac{1}{2})$,
where the weights are defined with respect to diffeomorphisms of a sphere in
momentum space. The Weyl equation thus appears as a consequence of the
transformation behavior of local sections of half--canonical bundles under a
change of charts. As a consequence, it is possible to impose covariant
constraints on spinors of negative (positive) helicity in terms of
(anti--)holomorphy conditions. Furthermore, the identification with
half--differentials is employed to determine possible extensions of fermion
propagators compatible with Lorentz covariance. This paper includes in
particular the full derivation of the primary correlators needed in order to
determine the fermion correlators.
