COMPLEXIFIED 2-SPINOR THEORY OF POSITIVE FREQUENCY DIRAC FIELDS

The equations of motion yielding the Van-der-Waarden form of the Dirac free-field theory in complex Minkowski space are actually derived by working out a variational principle that involves a manifestly two-spinor Lagrangian density. We make use of this Dirac Lagrangian density to build up a suitable defining relation for the energy-momentum tensor of the theory which gives rise at once to a set of essentially equivalent expressions for the tensor. In particular, it is shown that one of the structures arising from our definition coincides with the well-known Penrose expression up to a conventional overall sign. A set of new covariant contour integrals for the corresponding energy momentum four-vector and angular-momentum bivector is exhibited. We then show that the entire set of spinor formulae affords us another method of establishing the relevant charge-conservation statement.