Features of planar Lee-Wick electrodynamics

TL;DR

This paper investigates the unique features of planar Lee-Wick electrodynamics near a conducting line, revealing differences from higher-dimensional cases and showing the limitations of the image method in this context.

Contribution

It calculates the modified propagator and analyzes the interaction with a point charge, highlighting the distinct behavior in (2+1) dimensions and the impact on divergence control.

Findings

Interaction differs from (3+1)-dimensional Lee-Wick electrodynamics.

The image method is invalid in planar Lee-Wick electrodynamics.

Dimensional reduction enhances divergence suppression.

Abstract

In this letter we study some aspects of the planar Lee-Wick electrodynamics near a perfectly conducting line (unidimensional mirror). Specifically, the modified Lee-wick propagator due to the presence of a conducting line is calculated, and the interaction between the mirror and the point-like charge is investigated. It is shown that the behavior of this interaction is very different from the one already known for the $(3+1)$-dimensional Lee-Wick electrodynamics, where we have a planar mirror. It is also shown that the image method is not valid in planar Lee-Wick electrodynamics and the dimensional reduction yields a stronger taming of divergences.