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We quantize the macroscopic electromagnetic field in a system ofnon-dispersive polarizable bodies moving at constant velocities possiblyexceeding the Cherenkov threshold. It is shown that in general the quantizedsystem is unstable and neither has a ground state nor supports stationarystates. The quantized Hamiltonian is written in terms of quantum harmonicoscillators associated with both positive and negative frequencies, such thatthe oscillators associated with symmetric frequencies are coupled by aninteraction term that does not preserve the quantum occupation numbers.Moreover, in the linear regime the amplitudes of the fields may grow withoutlimit provided the velocity of the moving bodies is enforced to be constant.This requires the application of an external mechanical force that effectivelypumps the system.

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