Physical Fields in QED

TL;DR

This paper explores the relationship between two formulations of quantum electrodynamics (QED), revealing they are not directly gauge-equivalent and proposing an indirect connection through the Wightman reconstruction theorem.

Contribution

It clarifies the non-equivalence of Gupta-Bleuler and Coulomb gauge formulations of QED and introduces a novel approach linking them via the Wightman reconstruction theorem.

Findings

Gupta-Bleuler and Coulomb gauge formulations are not connected by a gauge transformation.

The Coulomb gauge state space cannot be embedded as a subspace of the Gupta-Bleuler space.

An indirect connection between the formulations is established through the Wightman reconstruction theorem.

Abstract

The connection between the Gupta-Bleuler formulation and the Coulomb gauge formulation of QED is discussed. It is argued that the two formulations are not connected by a gauge transformation. Nor can the state space of the Coulomb gauge be identified with a subspace of the Gupta-Bleuler space. Instead a more indirect connection between the two formulations via a detour through the Wightman reconstruction theorem is proposed.