  We develop a non-equilibrium field-theoretical approach, based on a
systematic diagrammatic expansion, for strongly interacting photons in
optically dense atomic media. We consider the case where the characteristic
photon-propagation range $L_P$ is much larger than the interatomic spacing $a$
and where the density of atomic excitations is low enough to neglect saturation
effects. In the highly polarizable medium the photons experience nonlinearities
through the interactions they inherit from the atoms. If the atom-atom
interaction range $L_E$ is also large compared to $a$, we show that scattering
processes with momentum transfer between photons are suppressed by a factor
$a/L_E$. We are then able to perform a self-consistent resummation of a
specific (Hartree-like) diagram subclass and obtain quantitative results in the
highly non-perturbative regime of large single-atom cooperativity. Here we find
important, conceptually new collective phenomena emerging due to the
dissipative nature of the interactions, which even give rise to novel phase
transitions. The robustness of these is investigated by inclusion of the
leading corrections in $a/L_E$. We consider specific applications to photons
propagating under EIT conditions along waveguides near atomic arrays as well as
within Rydberg ensembles.
