Light-Cone Path-Integral Approach
to the LandauPomeranchukMigdal Effect*

B. G. Zakharov¹⁾

Received November 27, 1997

Abstract—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 in terms of the Green’s function of a two-dimensional Schrödinger equation with an imaginary poten-
tial. In QED, this potential is proportional to the dipole cross section for the scattering of a e⁺e^– pair by an atom;
in QCD, it is proportional to the cross section for the interaction of a color-singlet quark–antiquark–gluon sys-
tem 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 E_q L², where L is the distance traveled by the quark in the medium. It has a weak
dependence on the initial quark energy E_q. The L² dependence transforms into L¹ as the quark energy decreases.
New formulas for nuclear shadowing in hard reactions are obtained.

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