Structure functions at small x from worldlines: Unpolarized distributions

The worldline representation of quantum field theory is a powerful framework for the computation of perturbative multileg 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, semiclassical approximations to quantum mechanical worldline trajectories provide useful intuition in a wide range of dynamical problems. We develop here the worldline approach to compute deeply inelastic structure functions in the small x Regge limit of QCD. 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 worldline computation of polarized structure functions at small x.