  The anomalous pseudoscalar-photon vertex is studied in real time in and out
of equilibrium in a constituent quark model. The goal is to understand the
in-medium modifications of this vertex, exploring the possibility of enhanced
isospin breaking by electromagnetic effects as well as the formation of neutral
pion condensates in a rapid chiral phase transition in peripheral,
ultrarelativistic heavy-ion collisions. In equilibrium the effective vertex is
afflicted by infrared and collinear singularities that require hard thermal
loop (HTL) and width corrections of the quark propagator. The resummed
effective equilibrium vertex vanishes near the chiral transition in the chiral
limit. In a strongly out of equilibrium chiral phase transition we find that
the chiral condensate drastically modifies the quark propagators and the
effective vertex. The ensuing dynamics for the neutral pion results in a
potential enhancement of isospin breaking and the formation of $\pi^0$
condensates. While the anomaly equation and the axial Ward identity are not
modified by the medium in or out of equilibrium, the effective real-time
pseudoscalar-photon vertex is sensitive to low energy physics.
