  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.
