Nonrelativistic Electron–electron Interaction in a Maxwell–chern–simons–proca Model Endowed With a Timelike Lorentz-Violating Background

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 electron-electron interaction is then exactly evaluated as the Fourier transform of the Möller scattering amplitude (carried out in the nonrelativistic limit) for the case of a purely timelike 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.

Classical kinematics for Lorentz violation

“…The 3-momentum and 3-velocity are typically noncollinear and their zeros noncoincident. When X < 0, the dispersion relation can be solved for p 0 to give p 0 = (p 2 ) 2 + (p 3 ) 2 ± √ −2X 2 + m 2 + (p 1 ) 2 (17) for the two positive sheets. The structure is similar to that reported in the case of timelike b µ [10], except that the sheets touch when the canonical momentum vanishes in the 2-3 plane rather than in all three momentum directions.…”

“…The kinematics of scattering in quantum field theory requires the exact propagator at all orders in Lorentz violation for external legs, essentially because the Lorentz-invariant states fail to span the asymptotic Hilbert space, and only a few processes have been analyzed (see, for example, Refs. [12][13][14][15][16][17][18][19]). The study of classical Lorentz-violating trajectories for bodies moving under electromagnetic fields and in postnewtonian gravity has been restricted to leading-order terms in Lorentz violation [20].…”