Causality in the Classical Limit for Quantum Electrodynamics

Abstract

We use the path integral form of quantum electrodynamics (QED) to show that a causal classical limit to QED can be derived by functionally integrating over the photon coordinates, starting from an initial photon vacuum and ending in a final coherent radiation state driven by the anticipated classical charged particle trajectories. The resulting charged particle transition amplitude depends only on particle coordinates. When the ${\hbar} \, \to \,0$ limit is taken, only those particle paths that are not constrained by the final radiation state are varied. These results demonstrate that the collapse from an infinity of charged particle paths, a path integral description, to causally interacting classical trajectories, a stationary-action description, is critically dependent on including final coherent state radiation and maintaining the distinction between particle paths that are free to vary and those trajectories that can be monitored by the final state radiation.