  The structure of singularities in perturbative massless gauge theories is
investigated in coordinate space. The pinch singularities in coordinate-space
integrals occur at configurations of vertices which have a direct
interpretation in terms of physical scattering of particles in real space-time
in the same way as for the loop momenta in the case of momentum-space
singularities. In the analysis of vertex functions in coordinate space, the
well-known factorization into hard, soft, and jet functions is found. By
power-counting arguments, it is found that coordinate-space integrals of vertex
functions have logarithmic divergences at worst.
