  In nonabelian gauge theory the three-gluon vertex function contains important
structural information, in particular on infrared divergences, and is also an
essential ingredient in the Schwinger-Dyson equations. Much effort has gone
into analyzing its general structure, and at the one-loop level also a number
of explicit computations have been done, using various approaches. Here we use
the string-inspired formalism to unify the calculations of the scalar, spinor
and gluon loop contributions to the one-loop vertex, leading to an extremely
compact representation in all cases. The vertex is computed fully off-shell and
in dimensionally continued form, so that it can be used as a building block for
higher-loop calculations. We find that the Bern-Kosower loop replacement rules,
originally derived for the on-shell case, hold off-shell as well. We explain
the relation of the structure of this representation to the low-energy
effective action, and establish the precise connection with the standard
Ball-Chiu decomposition of the vertex. This allows us also to predict that the
vanishing of the completely antisymmetric coefficient function S of this
decomposition is not a one-loop accident, but persists at higher loop orders.
The sum rule found by Binger and Brodsky, which leads to the vanishing of the
one-loop vertex in N=4 SYM theory, in the present approach relates to worldline
supersymmetry.
