Causal Propagation of Spin-Cascades

TL;DR

This paper demonstrates that the wave equations describing certain spin-cascades in electromagnetic fields are unconditionally hyperbolic and causal, resolving longstanding issues related to superluminal propagation in higher-spin theories.

Contribution

It proves that the wave equations for the (1/2,3/2) and (0,1,2) spin-cascades are unconditionally hyperbolic and causal, avoiding the Velo-Zwanziger problem.

Findings

Wave fronts propagate causally in the studied spin-cascades.

The equations are unconditionally hyperbolic.

The results extend to the direct product of two Proca equations.

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 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 proof that the irreducible spin-cascade embedded within four-vector 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.