Some theoretical aspects of observation of acceleration induced thermality

In recent work by Lynch, Cohen, Hadad, and Kaminer (LCHK), a modified model of the Unruh-DeWitt two-level quantum detector, coupled to a semiclassical four-vector current, has been proposed to examine the radiation emitted by high energy positrons channeled into silicon crystal samples. Inspired by their ideas, we analyze theoretical aspects of such a model, its internal consistency, and ignore all questions related to experiments. The two-potential correlation functions for the quantized electromagnetic field in a vacuum state and the corresponding detector radiation power (DRP), considered in proper time formalism, are used as the basis for investigating the radiation observed at an accelerating point detector. The quantum detector is assumed to be moving through an electromagnetic vacuum along a classical hyperbolic trajectory with a constant proper acceleration. The DRP is obtained for three possible cases. First, the DRP is found in a Lorentz-invariant manner. It contains both transverse and nonphysical longitudinal polarization modes and is a divergent quantity. Second, the radiation power holds only physical transverse modes, but it is nonrelativistic and also depends on the detector proper time, which contradicts the fact that there is no preferred time for hyperbolic detector motion. Third, in the particular case considered by LCHK, for zero detector proper time when its velocity in the lab inertial system is zero, the radiation power with transverse modes shows some signs of thermality that could be associated with a detector acceleration but different from the Bose-Einstein statistics expected for the photon field. If the detector energy gap is zero then, in complete contradiction with what LCHK claim, there is no radiation and no ``thermalized Larmor formula.'' Based on our analysis we do not believe that the LCHK's model can be used to support the idea about thermal effects of uniform acceleration.