CAUSAL PROPAGATION OF SPIN-CASCADES

Abstract

We gauge the direct product of the Proca with the Dirac equation that describes the coupling to the electromagnetic field of the spin-cascade (1/2, 3/2) residing in the four-vector spinor ψμ and analyze propagation of its wave fronts in terms of the Courant–Hilbert criteria. We show that the differential equation under consideration is unconditionally hyperbolic and the propagation of its wave fronts unconditionally causal. In this way we prove that the irreducible spin-cascade embedded within ψμ is free from the Velo–Zwanziger problem that plagues the Rarita–Schwinger description of spin-3/2. The proof extends also to the direct product of two Proca equations and implies causal propagation of the spin-cascade (0, 1, 2) within an electromagnetic environment.