First-order differential equations for a particle with spin $S=1$

Abstract

A system of first-order differential equations for a particle with nonzero mass and spin $S=1$ is constructed. As distinct from the Proca-Duffin-Kemmer (PDK) equations, the system has the form of the dynamical equation $i\hslash {\partial }_t\hat{\Psi }=\hat{\mathrm{H}}\hat{\Psi }$ (with constraints) with a Hamiltonian linear in momentum. The six-component wave function yields the positive-definite probability density ${\hat{\Psi }}^{†}\hat{\Psi }\ge 0$. The system of equations has much in common with the Dirac and Maxwell equations.