Light-cone path integral approach to the Landau-Pomeranchuk-Migdal effect

A new rigorous light-cone path integral approach to the Landau-Pomeranchuk-Migdal effect in QED and QCD is discussed. The rate of photon (gluon) radiation by an electron (quark) in a medium is expressed through the Green's function of a two-dimensional Schrodinger equation with an imaginary potential. In QED this potential is proportional to the dipole cross section for scattering of e+e- pair off an atom, in QCD it is proportional to the cross section of interaction of the color singlet quark-antiquark-gluon system with a medium constituent. In QED our predictions agree well with the photon spectrum measured recently at SLAC for 25 GeV electrons. In QCD for a sufficiently energetic quark produced inside a medium we predict the radiative energy loss proportional L^{2}, where L is the distance passed by the quark in the medium. It has a weak dependence on the initial quark energy. The L^{2} dependence transforms into L^{1} as the quark energy decreases. We also give new formulas for nuclear shadowing in hard reactions.