MAXWELL FIELD ON THE POINCARÉ GROUP

Abstract

The massless field of spin 1 is defined on the eight-dimensional configuration space; this space is a direct product of Minkowski space and of a two-dimensional complex sphere. Field equations for the spin-one field are derived from a Dirac-like Lagrangian separately for the translation group and Lorentz group parts. It is shown that a Dirac form of Maxwell equations (the so-called Majorana–Oppenheimer formulation of electrodynamics) follows directly from the field equations of translation group part. The photon field is realized via Biedenharn type functions on the Poincaré group. This allows us to consider both Dirac and Maxwell fields on an equal footing, as the functions on the Poincaré group.