Half-Differentials and Fermion Propagators

Details Half-Differentials and Fermion Propagators Half-Differentials and Fermion Propagators

1994-10-13

arxiv.org/abs/hep-th/9410099v1

Rev.Math.Phys. 7 (1995) 689-708

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, Latex, IASSNS-HEP-94/83

Scientific paper

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.

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