Note on gauge invariance and causal propagation
Interactions of gauge-invariant systems are severely constrained by several consistency requirements.One is the preservation of the number of gauge symmetries, another is causal propagation. For lower-spinfields, the emphasis is usually put on gauge invariance that happens to be very selective by itself. Wedemonstrate with an explicit example, however, that gauge invariance, albeit indispensable for constructinginteractions, may not suffice as a consistency condition. The chosen example that exhibits this featureis the theory of a massless spin-3=2 field coupled to electromagnetism.We show that this system admits anelectromagnetic background in which the spin-3=2 gauge field may move faster than light. Requiringcausal propagation rules out otherwise allowed gauge-invariant couplings. This emphasizes the importanceof causality analysis as an independent test for a system of interacting gauge fields. We comment onthe implications of allowing new degrees of freedom and nonlocality in a theory, on higher-derivativegravity and Vasiliev’s higher-spin theories.