Why Cerenkov Radiation May Not Occur, Even When It Is Allowed by Lorentz-Violating Kinematics

Brett Altschul

doi:10.3390/sym9110250

Abstract

In a Lorentz-violating quantum field theory, the energy-momentum relations for the field quanta are typically modified. This affects the kinematics, and processes that are normally forbidden may become allowed. One reaction that clearly becomes kinematically possible when photons’ phase speeds are less than 1 is vacuum Cerenkov radiation. However, in spite of expectations, and in defiance of phase space estimates, a electromagnetic Chern–Simons theory with a timelike Lorentz violation coefficient does not feature any energy losses through Cerenkov emission. There is an unexpected cancelation, made possible by the existence of unstable long-wavelength modes of the field. The fact that the theory possesses a more limited form of gauge symmetry than conventional electrodynamics also plays a role.

Highlights

Symmetry plays a critical role in our understanding of physics, especially the physics of particles and fields
This theory is known as the standard model extension (SME), and has an action that is constructed from all operators that may be built up from standard model fields [2,3]
The result that P is identically zero could be seen as quite puzzling. It seemed that there should at least be radiation emitted into the slow modes with |2k| < p

Summary

Introduction

Symmetry plays a critical role in our understanding of physics, especially the physics of particles and fields. Even without any experimental indication that violations of Lorentz or CPT symmetries are possible, studying exotic theories in which these symmetries do not hold can reveal a great deal about the general structure of quantum field theory. A single EFT describing both Lorentz and CPT violation has been the subject of extensive study over the past two decades This theory is known as the standard model extension (SME), and has an action that is constructed from all operators that may be built up from standard model fields [2,3]. The Chern–Simons theory is still of great theoretical interest, because it has some highly unusual features—features seen in few other quantum field theories Another of the most notable features is that the Chern–Simons Lagrange density is not gauge invariant on its own.

The Chern–Simons Term in Electrodynamics

Vanishing of the Cerenkov Rate

Concluding Remarks