Radiation field for a many-body system

Semi-classical radiation theory is used to derive possible radiation fields for a group of charged particles obeying quantum mechanics. One of these fields can only be produced by a system with two or more than two charged particles. The polarization of this field is determined by the vector potential of external driving field and the curl of velocity field. We show that the semi-classical results are the zero-order approximation of the non-relativistic quantum electrodynamics in the reaction of radiation fields. A classical analogue is suggested which clearly illustrates the origins of the sources of fields.