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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?

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    $\begingroup$ G. Velo, D. Zwanziger, Phys.Rev. 188 (1969) 2218-2222, dx.doi.org/10.1103/PhysRev.188.2218 $\endgroup$ Commented Aug 18, 2016 at 19:10
  • $\begingroup$ @CosmasZachos G Velo?? Oh my ... He is (was) my professor! I will go to him next week!! $\endgroup$
    – Les Adieux
    Commented Aug 18, 2016 at 19:20
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    $\begingroup$ @Beta, I think it would show great form for you to, after consulting with your professor, write up an answer to your question. $\endgroup$ Commented Aug 18, 2016 at 22:19
  • $\begingroup$ How would you test in reality whether a 3/2 spin system is "elementary"? Do you have an accelerator facility with energy beyond the LHC? Low energy systems with that spin certainly exist. They also certainly do not "just" couple to electromagnetism. So the trivial assumption that electromagnetic coupling is the only physics these systems respond to is completely false. As an experimentalist I would put this into the trash bin right there. I am sure a theorist can take that bin to the landfill. $\endgroup$ Commented Apr 4, 2023 at 22:45

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