  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.
