I am studying some paper about energy loss in p-A collisions and I always see coherent scattering and incoherent scattering term. What means "soft gluon radiation is fully coherent over the medium"?
I am not a theorist but in my understanding it is something anologous to what we have in hadron nucleus coherent or incoherent scattering. That is in case of coherent scattering the medium acts as one entity that is individual amplitudes add coherently;
Let me cite from Wiki: "A high energy particle undergoing multiple soft scatterings from a medium will experience interference effects between adjacent scattering sites. From uncertainty as the longitudinal momentum transfer gets small the particles wavelength will increase, if the wavelength becomes longer than the mean free path in the medium (the average distance between scattering sites) then the scatterings can no longer be treated as independent events, this is the LPM effect." So the answer is yes if some conditions (like small momentum transfers) are met.