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Quantization of the Electromagnetic Field in Non-dispersive Polarizable Moving Media above the Cherenkov Threshold

We quantize the macroscopic electromagnetic field in a system of non-dispersive polarizable bodies moving at constant velocities possibly exceeding the Cherenkov threshold. It is shown that in general the quantized system is unstable and neither has a ground state nor supports stationary states. The quantized Hamiltonian is written in terms of quantum harmonic oscillators associated with both positive and negative frequencies, such that the oscillators associated with symmetric frequencies are coupled by an interaction term that does not preserve the quantum occupation numbers. Moreover, in the linear regime the amplitudes of the fields may grow without limit provided the velocity of the moving bodies is enforced to be constant. This requires the application of an external mechanical force that effectively pumps the system.