The quantum corrections on the theory of transition radiation

A Scheme of quantum treatment for transition radiation is proposed. The Fresnel coefficients are adopted to describe the stationary states of electromagnetic fields near the interface between two mediums before a canonical field quantization procedure can be performed. Then an usual perturbation approach in field theory leads to the general expressions of radiation intensity in two different polarizations. The second order quantum corrections are ascribed to the existence of electron spin. Some concrete formulas for the cases of electron or monopole acrossing a metal surface are presented as well