Dirac-Like Wave Equations for Particles of Nonzero Rest Mass, and Their Quantization

Abstract

The basic algebraic structure of the Dirac equation for the electron is used as a model for wave equations for other particles of nonzero rest mass. Wave equations of the form $({\ensuremath{\gamma}}^{\ensuremath{\mu}}{\ensuremath{\nabla}}_{\ensuremath{\mu}}+m)\ensuremath{\psi}=0$, where the $\ensuremath{\gamma}$-matrices satisfy the usual Dirac anticommutation rules ${[{\ensuremath{\gamma}}_{\ensuremath{\mu}}, {\ensuremath{\gamma}}_{\ensuremath{\nu}}]}_{+}=2{g}_{\ensuremath{\mu}\ensuremath{\nu}}$ are then found for every positive integral and half-odd-integral spin. Wave equations of the above form describing multiple spin particles are also found. The improper transformations are given explicitly in their most general form, and quantization is performed. Finally, the vector meson field is treated as an example.