Describing Weyl neutrinos by a set of Maxwell-like equations

Abstract

In this note we show that Weyl’s theory of massless neutrinos can be formulated in a form closely parallel to Maxwell’s electromagnetism. The neutrino spinor wave function is explicitly represented in terms of its real and imaginary components. The Weyl equation then takes a form similar to a set of inhomogeneous Maxwell equations involving a particularlongitudinal source. We relate plane-wave solutions of these equations to those corresponding to actual neutrinos and anti-neutrinos, identifying the spinor components in each case. We briefly comment on the possibility of constructing simple supersymmetric models relating spin-(l/2) and spin-1 fields.