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

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.

16 pages

References in corpus (5)

• Sensitive polarimetric search for relativity violations in gamma-ray bursts
• Lorentz-violating electrodynamics and the cosmic microwave background
• Failure of Gauge Invariance in the Nonperturbative Formulation of Massless Lorentz-Violating QED
• Cerenkov Radiation in a Lorentz-Violating and Birefringent Vacuum
• Absence of Long-Wavelength Cerenkov Radiation With Isotropic Lorentz and CPT Violation

Cited by in corpus (7)

• Effects of CPT-odd terms of dimensions three and five on electromagnetic propagation in continuous matter
• (Gravitational) Vacuum Cherenkov Radiation
• Nonminimal planar electrodynamics modified by higher-derivative terms
• Problems with Lorentz Violation Originating From a Cosmologically Varying Pseudoscalar Field
• Radiation from an Oscillating Dipole in the Presence of Photon-Sector CPT and Lorentz Violation
• Vacuum Radiation in $z=2$ Lifshitz QED
• Vacuum Cherenkov radiation at finite temperature