Comparison between semiclassical gravity and semiclassical electrodynamics

Abstract

It is known how the equation of motion for a quantum tieid in a classical CUM spacetime can be derived as an approximation lo the Wheeler-DeWLtt equation. In order 10 obtain a better understanding of ths derivation, we develop an analogous approximation for quanrum electrodynamics. We show lhat quantum field lheory in an erternal, classical electromagnetic field can be oblained as a limiting case of quantum electrodynamics, by expanding the full wavefunctional in a power series in the coupling constant e2. The important difference in the yo derivalions is that unlike the metric, Lhe electromagnetic potential has to be scaled wilh respect to the coupling constant before the semiclassical limit can be obtained.