The optical theorem in action: radiation of an electron in a Lorentz-violating vacuum

Abstract

According to the optical theorem, the imaginary part of the one-loop radiative shift of the electron energy in an external field (IP1L) determines the total probability of photon emission by the electron. We calculate IP1L and then the probability and power of radiation of an electron in a constant background tensor field, which simulates the violation of Lorentz invariance in the framework of the Standard Model Extension. Using current experimental constraints on the background field strength, we show that the considered radiation effect can manifest itself under astrophysical conditions at ultrahigh electron energy.