  The computation of radiative energy loss in a finite size QCD medium with
dynamical constituents is a key ingredient for obtaining reliable predictions
for jet quenching in ultra-relativistic heavy ion collisions. We here present a
theoretical formalism for the calculation of the first order in opacity
radiative energy loss of a quark jet traveling through a finite size dynamical
QCD medium. We show that, while each individual contribution to the energy loss
is infrared divergent, the divergence is naturally regulated once all diagrams
are taken into account. Finite size effects are shown to induce a non-linear
path length dependence of the energy loss, recovering both the incoherent
Gunion-Bertsch limit, as well as destructive Landau-Pomeanchuk-Migdal limit.
Finally, our results suggest a remarkably simple general mapping between energy
loss expressions for static and dynamical QCD media.
