  We analyze the nucleon's Compton scattering amplitude in the
Dyson-Schwinger/Faddeev approach. We calculate a subset of diagrams that
implements the nonperturbative handbag contribution as well as all t-channel
resonances. At the quark level, these ingredients are represented by the quark
Compton vertex whose analytic properties we study in detail. We derive a
general form for a fermion two-photon vertex that is consistent with its
Ward-Takahashi identities and free of kinematic singularities, and we relate
its transverse part to the onshell nucleon Compton amplitude. We solve an
inhomogeneous Bethe-Salpeter equation for the quark Compton vertex in
rainbow-ladder truncation and implement it in the nucleon Compton scattering
amplitude. The remaining ingredients are the dressed quark propagator and the
nucleon's bound-state amplitude which are consistently solved from
Dyson-Schwinger and covariant Faddeev equations. We verify numerically that the
resulting quark Compton vertex and nucleon Compton amplitude both reproduce the
pion-photon transition form factor when the pion pole in the t-channel is
approached.
