  We construct the gauge invariant three-photon decay amplitude of
particle-antiparticle bound states modeled by the Dyson-Schwinger and
Bethe-Salpeter equations. Application to the quark-antiquark ($q\bar{q}$) bound
states is emphasized. An essential aspect of our formulation is that it applies
to any underlying quantum field theoretic model of the $q\bar{q}$ system, and
not just to models, like exact QCD, where the quark self-energy $\Sigma$
couples to the electromagnetic field solely via dressed quark propagators. In
this way, applications to effective field theories and other QCD motivated
models are envisioned. The three-photon decay amplitude is constructed by
attaching currents to all possible places in the Feynman diagrams contributing
to the dressed quark propagator. The gauge invariance of our construction is
thus a direct consequence of respecting the underlying structure of the quantum
field theory determining the dynamics. In the resultant expression for the
three-photon decay amplitude, all the basic ingredients consisting of the bound
state wave function, the final-state interaction $q\bar{q}$ $t$ matrix, the
dressed quark propagator, and dressed quark currents, are determined by a
universal Bethe-Salpeter kernel.
