  Motivated by the need to correct the potentially large kinematic errors in
approximations used in the standard formulation of perturbative QCD, we
reformulate deeply inelastic lepton-proton scattering in terms of gauge
invariant, universal parton correlation functions which depend on all
components of parton four-momentum. Currently, different hard QCD processes are
described by very different perturbative formalisms, each relying on its own
set of kinematical approximations. In this paper we show how to set up
formalism that avoids approximations on final-state momenta, and thus has a
very general domain of applicability. The use of exact kinematics introduces a
number of significant conceptual shifts already at leading order, and tightly
constrains the formalism. We show how to define parton correlation functions
that generalize the concepts of parton density, fragmentation function, and
soft factor. After setting up a general subtraction formalism, we obtain a
factorization theorem. To avoid complications with Ward identities the full
derivation is restricted to abelian gauge theories; even so the resulting
structure is highly suggestive of a similar treatment for non-abelian gauge
theories.
