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I was reading the quite nice answer of QMechanic on the topic of compact support tachyon fields not propagating faster than light, but this case is a rather simple one, free scalar field in flat space.

Are there any more general theorems on this? Let's say, for a field transforming under the tachyonic representation of the Poincaré group, given a finite region $U$ of a spacelike hypersurface $S$, and some initial conditions of the field $\Phi_0$ with compact support in $U$, would the evolution of the field remain of compact support in $J^+(U)$, and if not, under what circumstances would this be broken?

This is sticking with classical tachyonic fields to not have to deal with any further issues concerning tachyonic fields.

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