Semiclassical theory of high-energy particle radiation in external fields

The review is devoted to the semiclassical theory of radiation of fast charged particles in external fields. The relationships between the semiclassical, Born, eikonal and classical approximations are considered in the theories of scattering and radiation. The semiclassical approximation in different representations of quantum mechanics is studied. Schwinger's operator method, its generalization for a large recoil under radiation and an arbitrary external field, and the method of canonical transformations are outlined. Special attention is paid to the problem of boundary conditions in the semiclassical theory of radiation. Specifically, the problems of scattering and radiation are considered in the case when several classical trajectories satisfy the same boundary conditions. In this case interference phenomena occur that are similar to the rainbow scattering phenomenon. The semiclassical theory of coherent radiation of relativistic particles in aligned crystals is outlined. (orig.)