Abstract
The correspondence between operator formulations of perturbation theory for fields and the heuristic form of the path integral with a configuration-space measure is examined. The assumptions necessary to construct the path integral are cataloged and used to formulate the vacuum transition amplitude in path-integral form for both a Hermitian scalar field theory and quantum electrodynamics. It is shown that Gauss's law forces the heuristic path integral in the Coulomb gauge to represent a transition between two dressed states rather than asymptotic Fock vacuums. The relation of this formalism to scattering amplitudes defined by the Lehmann-Symanzik-Zimmermann formalism is discussed.
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