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 the 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.