We consider how Lorentz-violating interactions in the Faddeev-Popov ghost sector will affect scalar QED. The behavior depends sensitively on whether the gauge symmetry is spontaneously broken. If the symmetry is not broken, Lorentz violations in the ghost sector are unphysical, but if there is spontaneous breaking, radiative corrections will induce Lorentz-violating and gauge-dependent terms in other sectors of the theory.
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Brett Altschul (2006) studied this question.
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