Transformation properties of gauge invariance systems at the quantum level and an application

Abstract

According to Faddeev-Popov's rule of path integral quantization, the generating functional of Green function in configuration space for a gauge_invariant constrained system is formulated, transformation properties of a gauge_invariant system at the quantum level are derived and the problems of the conserved laws at the quantum level are discussed. the quantal transformation properties of electromagnetic field near the interface of dielectric media under the Poincar group are studied. It is pointed out that the transverse shift of the reflection and refraction of electromagnetic waves near the interface of dielectric media also occur at the quantum level, but the results of classical theory must be amended in quantum theory.