  The extended algebra of the free electromagnetic fields, including infrared
singular fields, and the almost radial gauge, both introduced earlier, are
postulated for the construction of the quantum electrodynamics in a Hilbert
space (no indefinite metric). Both the Dirac and electromagnetic fields are
constructed up to the first order (based on the incoming fields) as operators
in the Hilbert space, and shown to have physically well interpretable
asymptotic behavior in far past and spacelike separations. The Dirac field
tends in far past to the free incoming field, carrying its own Coulomb field,
but with no 'soft photon dressing'. The spacelike asymptotic limit of the
electromagnetic field yields a conserved operator field, which is a sum of
contributions of the incoming Coulomb field, and of the low energy limit of the
incoming free electromagnetic field. This should agree with the operator field
similarly constructed with the use of outgoing fields, which then relates these
past and future characteristics. Higher orders are expected not to change this
picture, but their construction needs a treatment of the UV question, which has
not been undertaken and remains a problem for further investigation.
