Relativistic wave equation for a massive charged particle with arbitrary spin

Abstract

In this paper we present a relativistic second-order differential wave equation for a charged massive particle that may have arbitrary spin. Thereby we make use of the chiral Pauli-Lubanski operator by help of which we obtain two separate wave equations including the electromagnetic field. They are associated with right- and left-chiral spinors, both of which are (2s + 1)-multiplets for a general spin $s \geq 1$ . We derive the corresponding Lorentz-invariant Lagrangian, and present the related spinorial eigen-functions for particles and anti-particles.