First-Order Vacuum Polarizability from the Principle of Causality

Abstract

A driving current induces in the vacuum a response current, but the response must not precede its cause. This application of the principle of causality enables one to derive the Pauli-Rose result for first-order vacuum polarization from the most elementary calculation in quantum electrodynamics: the absorption of a single photon (with $-k_{\alpha }{k}^{\alpha }>4\mathrm{}{k_m}^2$) by a negative-energy electron. This calculation is also given.