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Creators/Authors contains: "Gavassino, L."

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  1. We show that linear superpositions of plane waves involving a single-valued, covariantly stable dispersion relation $$\omega(k)$$ always propagate outside the lightcone, unless $$\omega(k) =a+b k$$. This implies that there is no notion of causality for individual dispersion relations, since no mathematical condition on the function $$\omega(k)$$ (such as the front velocity or the asymptotic group velocity conditions) can serve as a sufficient condition for subluminal propagation in dispersive media. Instead, causality can only emerge from a careful cancellation that occurs when one superimposes all the excitation branches of a physical model. This is shown to happen automatically in local theories of matter that are covariantly stable. 
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