The SO(3,3) group as a common basis for Dirac's and Proca's equations

Abstract

Dirac's and Proca's equations are unified in the sense that the algebras of Dirac γ-matrices and Duffin-Kemmerβ-matrices are shown to furnish two distinct matrix representations of the Lie algebra of the SO(3,3)-group. This fact is then interpreted as evidence for the classical picture of particles described by the above-mentioned equations to be a relativistic top. It is also argued that the shape of the top is rod-like.