  The world-line representation of quantum field theory is a powerful framework
for the computation of perturbative multi-leg Feynman amplitudes. In
particular, in gauge theories, it provides an efficient way, via point particle
Grassmann functional integrals, to compute spinor and color traces in these
amplitudes. Further, semi-classical approximations to quantum mechanical
world-line trajectories provide useful intuition in a wide range of dynamical
problems. We develop here the world-line approach to compute deeply inelastic
structure functions in the small x Regge limit of QCD. In particular, in a
shockwave approximation valid in this limit, we show how one recovers the
well-known dipole model for unpolarized structure functions. In a follow-up
work, we will discuss the world-line computation of polarized structure
functions at small x.
