Coulomb Potential in Podolsky-Carroll-Field-Jackiw Electrodynamics

TL;DR

This paper explores the combined effects of Podolsky's higher-derivative electrodynamics and the Carroll-Field-Jackiw Lorentz-violating model, analyzing photon propagation and scattering, revealing how CFJ terms can reintroduce divergences and affect interaction potentials.

Contribution

It derives the photon propagator in the combined Podolsky-CFJ framework and studies its impact on M"{o}ller scattering and the interaction potential, highlighting Lorentz violation effects.

Findings

CFJ contributions can reintroduce short-distance divergences suppressed by Podolsky's term.

Both spatial and timelike CFJ components affect the interaction potential nontrivially.

The combined model modifies photon dispersion and introduces anisotropy in the potential.

Abstract

Podolsky electrodynamics, a higher-derivative extension of Maxwell's theory characterized by the Podolsky parameter $\lambda=1/m$, which modifies the photon dispersion relation and regularizes short-distance divergences, is investigated. This framework is then coupled to the Carroll-Field-Jackiw (CFJ) model, in which a Lorentz-violating background four-vector is introduced. Within this extended electrodynamics, the photon propagator is obtained in the combined Podolsky-CFJ framework and subsequently applied to M\"{o}ller scattering. It is shown that the CFJ contribution can reintroduce the short-distance divergence suppressed by Podolsky's term. In the nonrelativistic limit, both the spatial component--which introduces a preferred direction in space and thus breaks isotropy--and the timelike component--which directly affects the dispersion relation--contribute nontrivially to the interaction potential.