Cherenkov Radiation with Massive, CPT-violating Photons

Abstract

The source of CPT-violation in the photon sector of the Standard Model Extension arises from a Chern-Simons-like contribution that involves a coupling to a fixed background vector field $k_{AF}^{\mu }$. These Lorentz- and CPT-violating photons have well-known theoretical issues that arise from missing states at low momenta when $k_{AF}^{\mu }$ is timelike. In order to make the theory consistent, a tiny mass for the photon can be introduced, well below current experimental bounds. The implementation of canonical quantization can then be implemented as in the CPT-preserving case by using the Stückelberg mechanism. We explicitly construct a covariant basis of properly-normalized polarization vectors at fixed three-momentum satisfying the momentum space field equations, in terms of which the vector field can be expanded. As an application of the theory, we calculate the Cherenkov radiation rate for the case of purely timelike $k_{AF}^{\mu }$, and find a radiation rate at high energies that has a contribution that does not depend on the mass used to regulate the photons.

References in corpus (5)

• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• Vacuum Cherenkov radiation in spacelike Maxwell-Chern-Simons theory
• On the consistency of Lorentz invariance violation in QED induced by fermions in constant axial-vector background
• No Vacuum Cerenkov Radiation Losses in the Timelike Lorentz-Violating Chern-Simons Theory
• Absence of Long-Wavelength Cerenkov Radiation With Isotropic Lorentz and CPT Violation

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