  A non-perturbative and exactly solvable quantum field theoretical model for a
"dressed Dirac field" is presented, that exhibits all the kinematical features
of QED: an appropriate delocalization of the charged field as a prerequisite
for the global Gauss Law, superselected photon clouds (asymptotic expectation
values of the Maxwell field), infraparticle nature of charged particles that
cannot be separated from their photon clouds, broken Lorentz symmetry. The
model serves as an intermediate leg on a new roadmap towards full QED,
formulated as an off-shell theory, i.e., including a perturbative construction
of its interacting charged fields. It also fills a gap in recent discussions of
the "Infrared Triangle", and points the way towards a new scattering theory for
theories with massless particles of helicity $\geq 1$, in which infraparticles
can be described at the level of charged fields, rather than just states.
