Investigation of charged particles radiation moving in a homogeneous dispersive medium

In this work, we use Drude-Lorents model description to study the radiation of a charged particles moving in a homogeneous dispersive medium. A suitable quantized electromagnetic field for such medium is utilized to obtain proper equations for energy loss of the particle per unit length. The energy loss is separately calculated for transverse and longitudinal components of the filed operators. The calculations show that the longitudinal component of the field operators contributes in electron radiation, when dielectric function is exceedingly dependent on the frequency. It is also shown that when the dispersion is not included, the obtained equations are in a good agreement with previous results. For negligible dispersion, the contribution of the field's longitudinal component tends to zero and at the end the results are in agreement with Ginsberg's calculations. This calculation can reveal a development for the fields' quantization for permeable dielectric background medium.