  Potential non-relativistic Quantum Electrodynamics and the Keldysh-Schwinger
formalism is used to derive Kadanoff-Baym-like equations for two-body field
correlators. These cover the out-off-equilibrium dynamics and spectrum of heavy
particle-antiparticle pairs under ultra-soft transitions inside a plasma
background, whose temperature is much smaller compared to the typical relative
pair momentum. It is shown that the dynamical equation for the pair phase-space
distribution function, containing recombination and dissociation via the
electric dipole interactions, is consistent with the previous open quantum
system treatment of bound states in the Coulomb limit of the two-body spectral
function.
