  Soft photons produced in heavy ion collisions are an important tool for
probing the properties of the quark-gluon plasma. It is therefore crucial to
understand the background - soft photons produced in elementary collisions. Low
theorem states that soft photon production in hadron collisions is dominated by
Bremsstrahlung off charged initial and final state hadrons. Surprisingly,
almost every experiment observed an enhancement (by a factor of $2\div 5$)
above Low theorem's prediction. This is the longstanding puzzle of "anomalous
soft photon production." The phenomenon is not observed in processes with
leptonic final states, which suggests that the mechanism is due to
nonperturbative QCD evolution. We study this phenomenon using an exactly
soluble, massless, Abelian model in $1+1$ dimensions which shares with QCD many
important properties: confinement, chiral symmetry breaking, axial anomaly and
$\theta$-vacuum. We then apply this model to the soft photon production in the
fragmentation of jets produced in $Z^0$ decays and find a qualitative agreement
with the data.
