  The equations for Yang-Mills field in a medium are derived in a linear
approximation with respect to the gauge coupling parameter and the external
field. The obtained equations closely resemble the macroscopic Maxwell
equations. A canonical quantization is performed for a family of Fermi-like
gauges in the case of constant and diagonal (in the group indices) tensors of
electric permittivity and magnetic permeability. The physical subspace is
defined and the gauge field propagator is evaluated for a particular choice of
the gauge. The propagator is applied for evaluation of the cross-section of
ellastic quark scattering in the Born approximation. Possible applications to
Cherenkov-type gluon radiation are commented briefly.
