I've recently come around the study of the so called Rarita-Schwinger equation for elementary particles of spin $3/2$.
The point it the article is really short, and no book treats the topic in a very complete way. At a certain point, it says that
"Rarita–Schwinger Lagrangian coupled to electromagnetism leads to equation with solutions representing wavefronts, some of which propagate faster than light. In other words, the field then suffers from acausal, superluminal propagation; consequently, the quantization in interaction with electromagnetism is essentially flawed."
It gives no references and no proof of that, and I couldn't find anything.
So I was wondering: does this preclude the existence of spin 3/2 elementary particles? Or did someone manage to solve that bug?