Mode Analysis for Energetics of a Moving Charge In Lorentz- and CPT-Violating Electrodynamics

TL;DR

This paper investigates the energy dynamics of a moving charge in Lorentz- and CPT-violating electrodynamics, revealing how long-wavelength modes carry negative energy to cancel out radiation, explaining the absence of energy loss.

Contribution

It explicitly demonstrates the cancellation of energy in Lorentz- and CPT-violating electrodynamics through Fourier analysis of the fields, confirming the vanishing radiation rate.

Findings

Fourier transforms show sign change between small and large wave numbers.

Long-wavelength modes carry negative energy.

Energy cancellation explains no net radiation loss.

Abstract

In isotropic but Lorentz- and CPT-violating electrodynamics, it is known that a charge in unifom motion does not lose any energy to Cerenkov radiation. This presents a puzzle, since the radiation appears to be kinematically allowed for many modes. Studying the Fourier transforms of the most important terms in the modified magnetic field and Poynting vector, we confirm the vanishing of the the radiation rate. Moreover, we show that the Fourier transform of the field changes sign between small and large wave numbers. This enables modes with very long wavelengths to carry negative energies, which cancel out the positive energies carried away by modes with shorter wavelengths. This cancelation had previously been inferred but never explicitly demonstrated.