Maxwell field on the Poincare group

TL;DR

This paper formulates Maxwell's equations on an extended Poincaré group space, deriving a Dirac-like Lagrangian and unifying photon and Dirac fields as functions on the group, offering a novel geometric perspective.

Contribution

It introduces a new framework for describing Maxwell fields on the Poincaré group, deriving field equations from a Dirac-like Lagrangian, and unifying photon and Dirac fields geometrically.

Findings

Maxwell equations are derived in a Dirac-like form from the Poincaré group structure.

Photon fields are represented via Biedenharn type functions on the Poincaré group.

The approach unifies Dirac and Maxwell fields as functions 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 (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 Poincar\'{e} group. This allows us to consider both Dirac and Maxwell fields on an equal footing, as the functions on the Poincar\'{e} group.