We study the dynamics of quantum fluctuations which take place at the
earliest stage of high-energy processes and the conditions under which the data
from e-p deep-inelastic scattering may serve as an input for computing the
initial data for heavy-ion collisions at high energies. Our method is
essentially based on the space-time picture of these seemingly different
phenomena. We prove that the ultra-violet renormalization of the virtual loops
does not bring any scale into the problem. The scale appears only in connection
with the collinear cut-off in the evolution equations and is defined by the
physical properties of the final state. In heavy-ion collisions the basic
screening effect is due to the mass of the collective modes (plasmons) in the
dense non-equilibrium quark-gluon system, which is estimated. We avoid the
standard parton phenomenology and suggest a dedicated class of evolution
equations which describe the dynamics of quantum fluctuations in heavy-ion
collisions.Comment: 54 pages, 11 Postscript figures, uses RevTe
