Radiation by wave packets

We calculate the energy radiated by Lorentz electrons accelerated in uniform electromagnetic fields up to O(ℏ). The quantum state for the Lorentz electron is chosen to be some wave packet with the expectation value of the position identical to the classical trajectory. We find that the quantum correction includes two parts: the radiative dissipation to the background, which depends on the configuration of the wave packet, and the absorption from the background fluctuation, which is proportional to the background field strength. In the case of an electron linearly accelerated in a uniform electric field, the absorption vanishes. Hence one cannot see the trace of the Unruh radiation by observing the radiation emitted by the uniformly accelerated wave packets.