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