The Lehmann-Symanzik-Zimmermann Formalism for Manifestly Covariant Quantum Electrodynamics

Abstract

The Lehmann-Symanzik-Zimmermann formalism is presented for manifestly covariant quantum electrodynamics involving a gauge parameter α. Contrary to Källén's assertion, it is shown that one can consistently formulate the asymptotic condition for the electromagnetic field and construct the Fock space of asymptotic states. Except for the case of Feynman gauge (α=1), the formalism is somewhat complicated because of the presence of dipole ghosts, but emphasis is laid on the very existence of a consistent formalism. The completeness relation for the asymptotic states is presented so that the generalized unitarity relation can be written down. Indefinite-metric theory of a massive vector field is briefly discussed.