HALF-DIFFERENTIALS AND FERMION PROPAGATORS

DOI10.1142/S0129055X9500027XzbMATH Open0867.53062arXivhep-th/9410099MaRDI QIDQ4848273

Rainer Dick

Publication date: 14 August 1997

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Abstract: From a geometric point of view, massless spinors in $3+1$ dimensions are composed of primary fields of weights $(frac12,0)$ and $(0,frac12)$, 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.

Full work available at URL: https://arxiv.org/abs/hep-th/9410099

zbMATH Keywords

Weyl equationmassless spinor fieldsfermionic propagatorshalf-differentials

Mathematics Subject Classification ID

Quantum field theory on curved space or space-time backgrounds (81T20) Applications of differential geometry to physics (53Z05) Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism (83C60)

Related Items (2)

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