Radiation of a Relativistic Charge in a Plane wave Electromagnetic Field

The radiation of a charge moving in the field of a plane circularly polarized electromagnetic wave is discussed by the methods of classical and quantum theory both for a zeropin particle (boson) and for an electron. Such considerations allow us to analyse the role of quantum and spin effects on the radiation. It is shown that the present problem has deep analogies with the problem of the synchrotron radiation. From this point of view many physical features of COMPTON radiation are represented as simple consequences of the classical or quantum theory of synchrotron radiation.