In-medium QCD and Cherenkov gluons

The equations of in-medium gluodynamics are proposed. Their classical lowest order solution is explicitly shown for a color charge moving with constant speed. For nuclear permittivity larger than 1 it describes emission of Cherenkov gluons resembling results of classical electrodynamics. The choice of nuclear permittivity and Lorentz-invariance of the problem are discussed. Effects induced by the transversely and longitudinally moving (relative to the collision axis) partons at LHC energies are described.