The indefinite metric space 𝒪M of the covariant form of the quantized Maxwell field M is analyzed in some detail. 𝒮M contains not only the pre-Hilbert space 𝒳0 of states of transverse photons which occurs in the Gupta–Bleuler formalism of the free M, but a whole rosette of continuously many, isomorphic, complete, pre-Hilbert spaces ℒq disjunct up to the zero element o of 𝒮M. The ℒq are the maximal subspaces of 𝒮M which allow the usual statistical interpretation. Each ℒq corresponds uniquely to one square integrable, spatial distribution jo(x) of the total charge Q=0. If M is in any state from ℒq, the bare charge j0(x) appears to be inseparably dressed by the quantum equivalent of its proper, classical Coulomb field E(x). The vacuum occurs only in the state space ℒ0 of the free Maxwell field. Each ℒq contains a secondary rosette of continuously many, up to o disjunct, isomorphic Hilbert spaces ℋgq related to different electromagnetic gauges. The space ℋoq, which corresponds to the Coulomb gauge within the Lorentz gauge, plays a physically distinguished role in that only it leads to the usual concept of energy. If M is in any state from ℋgq, the bare 4-current j0(x), j(x), where j(x) is any square integrable, transverse current density in space, is endowed with its proper 4-potential which depends on the chosen gauge, and with its proper, gauge independent, Coulomb–Oersted field E(x), B(x). However, these fields exist only in the sense of quantum mechanical expectation values equipped with the corresponding field fluctuations. So they are basically different from classical electromagnetic fields.