On the connection between acausal propagation and the non-local structure of higher spin fields

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Abstract
We show that a free spin 3/2 theory of the Pauli–Fierz type displays nonlocal structure. Similarly, a spin 1 theory coupled via an electric quadrupole to an external field also shows nonlocal structure. This is in sharp contrast to the cases of spin 0, 1/2, and 1 which do not have any nonlocality even in the presence of minimal coupling to an electromagnetic field. This leads us to conjecture that the acausal propagation discovered for spin 3/2 and spin 1 is due to additional structure of these fields.

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