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We study the impact of Lorentz violating terms on a physical observable forboth electrodynamics of chiral matter and an Abelian Higgs-like model in $3+1$dimensions. Our calculation is done within the framework of thegauge-invariant, but path-dependent, variables formalism. Interestingly enough,for electrodynamics of chiral matter we obtain a logarithmic correction to theusual static Coulomb potential. Whereas for a Abelian Higgs model with aLorentz-breaking term, our result displays new corrections to the Yukawapotential.

Remarks on the static potential in theories with Lorentz violation terms