  We develop a coordinate version of light-cone-ordered perturbation theory,
for general time-ordered products of fields, by carrying out integrals over one
light-cone coordinate for each interaction vertex. The resulting expressions
depend on the lengths of paths, measured in the same light-cone coordinate.
Each path is associated with a denominator equal to a "light-cone deficit",
analogous to the "energy deficits" of momentum-space time- or
light-cone-ordered perturbation theory. In effect, the role played by
intermediate states in momentum space is played by paths between external
fields in coordinate space. We derive a class of identities satisfied by
coordinate diagrams, from which their imaginary parts can be derived. Using
scalar QED as an example, we show how the eikonal approximation arises
naturally when the external points in a Green function approach the light cone,
and we give applications to products of Wilson lines. Although much of our
discussion is directed at massless fields in four dimensions, we extend the
formalism to massive fields and dimensional regularization.
