Physical Fields in QED

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.