The theory of the Landau, Pomeranchuk, Migdal effect

Bremsstrahlung of photons from highly relativistic electrons is investigated. The cross section of the processes, which is suppressed due to a multiple scattering of an emitting electron in dense media (LPM effect) and due to photon interaction with electrons of a medium, is calculated with an accuracy up to "next to leading logarithm" and with the Coulomb corrections taken into account. Making allowances for a multiple scattering and a polarization of a medium an analysis of radiation on a target boundary is carried out. The method of consideration of radiation in a thin target under influence of the LPM effect is developed. Interrelation with the recent experiment is discussed.