Two-spinor formulation of the theory of classical Maxwell-Dirac fields in curved space-times without torsion

Summary

The two-component spinor version of the theory of classical Maxwell-Dirac fields in curved space-times without torsion is presented. The pertinent dynamical statement thus involves an invariant Lagrangian density which implicitly carries the affine connections that enter into the conventional relativistic spinor structures. It is shown explicitly how the natural couplings between photons, electrons and gravitons arise automatically out of the actual derivation of the wave equations for the fields. At this stage the procedures actually include making use of calculational devices which are built up from a new set of geometric formulae. It is particularly pointed out that the wave equations can be rewritten in a more transparent form by utilizing certain covariant-derivative relations.