  We present the BFKL equation as a reggeon Bethe-Salpeter equation and discuss
the use of reggeon diagrams to obtain 2-2 and 2-4 reggeon interactions at
$O(g^4)$. We then outline the dispersion theory basis of multiparticle
$j$-plane analysis and describe how a gauge theory can be studied by combining
Ward identity constraints with the group structure of reggeon interactions. The
derivation of gluon reggeization, the $O(g^2)$ BFKL kernel, and $O(g^4)$
corrections, is described within this formalism. We give an explicit expression
for the $O(g^4)$ forward ``parton'' kernel in terms of logarithms and evaluate
the eigenvalues. A separately infra-red finite component with a holomorphically
factorizable spectrum is shown to be present and conjectured to be a new
leading-order partial-wave amplitude. A comparison is made with Kirschner's
discussion of $O(g^4)$ contributions from the multi-Regge effective action.
