Velo–Zwanziger problem

There are consistency problems with the classical theory of a massive spin 3/2 particle, described by the Rarita-Schwinger equation and interacting with an electromagnetic field, which manifest as a breakdown of the causal structure of the theory, because there are solutions of the equations of motion that propagate faster than light. More generally, a conventional Rarita-Schwinger spinor field minimally coupled to a gauge field admits superluminal solutions over backgrounds with nonzero gauge curvature. An alternative formulation of the problem states that the massive Rarita-Schwinger field cannot be consistently coupled to a gauge field.

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Further reading

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