Complexified two-component spinor theory of Dirac-Weyl fields

Abstract

A method whereby one may actually work out a variational principle involving a Lagrangian density in complex Minkowski space is used to derive the explicit two-spinor equations of motion for positive-frequency free electron neutrino fields. We build up a defining relation for the energy-momentum tensor of the theory which directly yields the well-known Penrose expression when only left-handed neutrinos are taken into consideration. It is shown explicitly that this tensor appears to fulfil the usual requirements of symmetry, trace-freeness and divergencelessness. A set of manifestly covariant integral expressions for the corresponding energy-momentum four-vector and angular-momentum bivector is then exhibited.