  Some considerations about the importance of coherence effects for
bremsstrahlung processes in non--equilibrium dense matter (Landau - Pomeranchuk
- Migdal - effect) are presented. They are of particular relevance for the
application to photon - and di-lepton production from high energy nuclear
collisions, to gluon radiation in QCD transport, or parton kinetics and to
neutrino and axion radiation from supernova explosion and from hot neutron
stars. The soft behavior of the bremsstrahlung from a source described by
classical transport models is discussed and pocket correction formulas for the
in-matter radiation cross sections are suggested in terms of standard transport
coefficients. The radiation rates are also discussed within a non--equilibrium
quantum field theory (Schwinger - Kadanoff - Baym - Keldysh) formulation. A
classification of diagrams and corresponding resummation in physically
meaningful terms is proposed, which considers the finite damping width of all
source particles in matter. This way each diagram in this expansion is already
free from the infra--red divergences. Both, the correct quasi--particle and
quasi--classical limits are recovered from this subset of graphs. Explicit
results are given for dense matter in thermal equilibrium. The diagrammatic
description may suggest a formulation of a transport theory that includes the
propagation of off--shell particles in non--equilibrium dense matter.
