### Abstract

The indefinite metric spaceO_{ M } of the covariant form of the quantized Maxwell field *M* is analyzed in some detail. S_{ M } contains not only the pre‐Hilbert space X^{0} of states of transverse photons which occurs in the Gupta–Bleuler formalism of the *f* *r* *e* *e* *M*, but a whole rosette of continuously many, isomorphic, complete, *p* *r* *e*‐*H* *i* *l* *b* *e* *r* *t* *s* *p* *a* *c* *e* *s*L^{ q } disjunct up to the zero element *o* of S_{ M }. The L^{ q } are the maximal subspaces of S_{ M } which allow the usual statistical interpretation. Each L^{ q } corresponds uniquely to one square integrable, spatial distribution *j* ^{ o }(x) of the total charge *Q*=0. If *M* is in *a* *n* *y* state from L^{ q }, the bare charge *j* ^{0}(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 L^{0} of the free Maxwell field. Each L^{ q } contains a secondary rosette of continuously many, up to *o* disjunct, isomorphic *H* *i* *l* *b* *e* *r* *t* *s* *p* *a* *c* *e* *s*H_{ g } ^{ q } related to different electromagnetic gauges. The space H_{ o } ^{ q }, 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 H_{ g } ^{ q }, the bare 4‐current *j* ^{0}(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 *c* *l* *a* *s* *s* *i* *c* *a* *l*electromagnetic fields.

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