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From a geometric point of view, massless spinors in $3+1$ dimensions arecomposed 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 inmomentum space. The Weyl equation thus appears as a consequence of thetransformation behavior of local sections of half--canonical bundles under achange of charts. As a consequence, it is possible to impose covariantconstraints on spinors of negative (positive) helicity in terms of(anti--)holomorphy conditions. Furthermore, the identification withhalf--differentials is employed to determine possible extensions of fermionpropagators compatible with Lorentz covariance. This paper includes inparticular the full derivation of the primary correlators needed in order todetermine the fermion correlators.Comment: 22 pages, Latex, IASSNS-HEP-94/8

HALF-DIFFERENTIALS AND FERMION PROPAGATORS