In the Podolsky-CFJ model the CFJ term reintroduces short-distance divergences and produces a nonrelativistic Coulomb potential that breaks isotropy and alters the dispersion relation.
Podolsky electromagnetism at finite temperature: Implications on the Stefan-Boltzmann law,
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Coulomb Potential in Podolsky-Carroll-Field-Jackiw Electrodynamics
In the Podolsky-CFJ model the CFJ term reintroduces short-distance divergences and produces a nonrelativistic Coulomb potential that breaks isotropy and alters the dispersion relation.