Soft gluon radiation induced by multiple scattering of a fast quark or gluon propagating through QCD matter is discussed. After revisiting the Landau-Pomeranchuk-Migdal effect in QED we show that large formation times of bremsstrahlung quanta determine the QCD radiation intensity (in analogy to QED) and derive the gluon energy spectrum. Coherent suppression takes place as compared to the Bethe-Heitler situation of independent emissions. As a result the energy loss of fast partons in a QCD medium depends on the incident energy E similarly to QED, −dE/dz ∝ √ E. † Permanent address: Petersburg Nuclear Physics Institute,

We extend the BDMPS formalism for calculating radiative energy loss to the case when the radiated gluon carries a finite fraction of the quark momentum. Some virtual terms, previously overlooked, are now included. The equivalence between the formalism of BDMPS and that of B. Zakharov is explicitly demonstrated.

The calculation of the radiative energy loss encountered by a fast charged particle which undergoes multiple scattering is being investigated. A detailed derivation of the Landau-Pomeranchuk-Migdal coherent effect in QED is given, focusing on the specific feature of the Coulomb interaction. As a result the radiation intensity per unit length in the coherent regime is shown to be proportional to $\sqrt \omega$ for a photon energy $\omega$ times a logarithmic enhancement which is determined exactly.Comment: 19 pages, LaTeX styl

The induced momentum spectrum of soft gluons radiated from a high energy quark propagating through a QCD medium is derived in the BDMPS formalism. A calorimetric measurement for the medium dependent energy lost by a jet with opening angle θcone is proposed.The fraction of this energy loss with respect to the integrated one appears to be the relevant observable.It exhibits a universal behaviour in terms of the variable θ 2 cone L 3q where L is the size of the medium andq the transport coefficient. Phenomenological implications for the differences between cold and hot QCD matter are discussed.12.38. Bx, 12.38.Mh, 24.85.+p,

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