In isotropic but Lorentz- and CPT -violating electrodynamics, it is known that a charge in uniform 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 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.
Published in Physical Review D, Volume 97, Issue 5, 2018, pages 055029-1-055029-9.
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
DeCosta, R., & Altschul, B. (2018). Mode Analysis for Energetics of a Moving Charge in Lorentz- and CPT-Violating Electrodynamics. Physical Review D, 97(5), 055029. https://doi.org/10.1103/PhysRevD.97.055029