Non-relativistic electron-electron interaction in a Maxwell-Chern-Simons-Proca model endowed with a timelike Lorentz-violating background

TL;DR

This paper investigates electron-electron interactions in a planar Maxwell-Chern-Simons-Proca model with Lorentz violation, revealing attractive potentials that could lead to bound states, using exact Fourier transform methods in the non-relativistic limit.

Contribution

It provides an exact calculation of the electron-electron interaction potential in a Lorentz-violating framework, highlighting the potential for bound state formation.

Findings

Interaction potential is totally screened at large distances.

Total interaction can be attractive, suggesting bound states.

Massive mediators lead to short-range interactions.

Abstract

A planar Maxwell-Chern-Simons-Proca model endowed with a Lorentz-violating background is taken as framework to investigate the electron-electron interaction. The Dirac sector is introduced exhibiting a Yukawa and a minimal coupling with the scalar and the gauge fields, respectively. The the electron-electron interaction is then exactly evaluated as the Fourier transform of the Moller scattering amplitude (carried out in the non-relativistic limit) for the case of a purely time-like background. The interaction potential exhibits a totally screened behavior far from the origin as consequence of massive character of the physical mediators. The total interaction (scalar plus gauge potential) can always be attractive, revealing that this model may lead to the formation of electron-electron bound states.