ℏ→0limit of quantum electrodynamics

Using a two-step procedure, we construct the $\hslash \to 0$ limit of quantum electrodynamics: (1) We functionally integrate away the photon coordinates in the transition amplitude to a general particle state with radiation. (2) We then take the $\hslash \to 0$ limit, using care to vary only those particle variables which have not been specified in defining the final radiation state.