Quantum Cherenkov radiation by spinless and spin-1/2 particles

In this paper, the Cherenkov radiation process is investigated in the frame of the Quantum Field Theory, both for the spinless and spin-1/2 charged particles. In the latter case, the polarization density matrix technique was used to account for the spin flip. If compared with the Classical Electrodynamics results, in both cases several quantum corrections arise, coinciding up to the photon's energy linear term. It is shown that, while the absolute value of these corrections significantly relies on the refractive index, the relative quantum correction stays independent of the medium in the case of the ultrarelativistic particles. It the case of the spin-1/2 particles it turns out that the spin flip practically never occurs in this process. For both cases, spinless and spin-1/2, the outgoing photon polarization vector lies always in the plane formed by the initial particle's momentum vector and the final photon's wave vector.