Quantum Electrodynamics of Čerenkov Radiation at Finite Temperature

An exact, to order α, study of Čerenkov radiation in QEDis carried out at finitetemperatures T ≠ 0 in isotropic homogeneous media for the first time. By avoidingthe method of combining denominators of Feynman propagators in parametricform, which has led to approximations in the past due to the complexity of theresulting integrals, we use instead a complex integration method and automaticallyevaluate the h2ω2/E2contribution to the quantum power spectrum and settle theambiguity associated with this term which has been known to exist at T = 0.We show that complex integration over a so-called pinching singularity actuallysimplifies the problem tremendously over the usual method of combining thedenominators of the propagators. In particular, the imaginary part of the electronself-energy satisfies the correct underlying boundary condition and no contactterm is needed in its evaluation. QED, unlike its classical counterpart, introducesautomatically a cutoff for higher frequencies, emphasizing the importance of thequantum treatment.