Wave Equations for Particles with Arbitrary Spins

Abstract

Here we want to outline briefly how to construct wave functions which describe particles with spin $s = 1,\;\frac{2} {3}, \ldots$ out of solutions of the Dirac equation and also to study by what kind of wave equation they are generated. As already seen in Chap. 6, the lower components of free solutions of the Dirac equation with positive energy vanish in the case m ₀ ≠ 0 in the rest system of the particles [cf. (6.13)]. Thus, for E _p = m ₀ c ² (which means p _i = 0 when we are in the rest system) the spinor components are given by ω ^(r)_α (0) = δ rα and thus

$$ \omega _\alpha ^{\left( + \right)} = 0,\;\;\;\;\alpha = 3,4. $$