Non-local material vacuum and Cherenkov radiation in non-linear massive $3$D-Electrodynamics

TL;DR

This paper explores how non-linearities in 3D electrodynamics alter vacuum properties, leading to non-local behavior and Cherenkov radiation, influenced by the de Broglie-Proca mass term.

Contribution

It introduces a detailed analysis of non-local vacuum effects and Cherenkov radiation in non-linear 3D electrodynamics, emphasizing the role of the mass term.

Findings

Vacuum exhibits spatially-dispersive, non-local characteristics.

Non-linearities modify permittivity, susceptibility, and refractive index.

Cherenkov radiation occurs due to medium interactions in non-linear electrodynamics.

Abstract

We examine the effects of electromagnetic field non-linearities in $3$ space-time dimensions. We focus on how these non-linearities influence permittivity and susceptibility. This, in turn, leads to changes in the refractive index through the use of the dispersion relation in the context of massless and massive non-linear electrodynamics. We also verify that, by inspecting the model addressed in the frequency/wave vector space, we identify the characteristics of a non-local material in the behavior of the vacuum, which exhibits a spatially-dispersive profile. Furthermore, it is important to highlight that the cause of this phenomenon is the de Broglie-Proca mass term. We subsequently investigate the electromagnetic radiation emitted by a moving charged particle interacting with a medium for massless and massive non-linear electrodynamics. Our findings indicate that the radiation is driven by the medium through which the particle travels, similar to what is observed in the Cherenkov effect.