A COMPARISON BETWEEN SEMICLASSICAL GRAVITY AND SEMICLASSICAL ELECTRODYNAMICS

It is known how the equation of motion for a quantum field in a classical curved spacetime can be derived as an approximation to the Wheeler-DeWitt equation. In order to obtain a better understanding of this derivation, we develop an analogous approximation for quantum electrodynamics. We show that quantum field theory in an external, classical electromagnetic field can be obtained as a limiting case of quantum electrodynamics, by expanding the full wave-functional in a power series in the coupling constant e2. The important difference in the two derivations is that unlike the metric, the electromagnetic potential has to be scaled with respect to the coupling constant before the semiclassical limit can be obtained.