Functional Schrödinger equation for scalar QED

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Abstract
We present an approximation scheme which, starting from the full functional Schrödinger equation for scalar QED, leads to the approximation of quantum field theory in a classical electromagnetic background. We solve the functional Schrödinger equation in this background exactly for evolving vacuum states. We show how well-known effects such as pair creation in a constant external electric field and dispersion are recovered in this framework. We give explicit results for the phase of the wave functional in two-dimensional QED. The next order of approximation leads to expressions for QED corrections to the external-field Schrödinger equation and for back-reaction effects of the matter field on the classical background. We discuss these terms and give explicit expressions for special cases. Contact is also made to a description in terms of Feynman diagrams. We finally comment on the analogous situation in quantum gravity.