  We relate the structure functions of deep inelastic lepton-nucleon scattering
to current-current correlation functions in a Euclidean field theory depending
on a parameter r. The r-dependent Hamiltonian of the theory is P0-(1-r)P3, with
P0 the usual Hamiltonian and P3 the third component of the momentum operator.
We show that small x in the structure functions correspond to the small r limit
of the effective theory. We argue that for r->0 there is a critical regime of
the theory where simple scaling relations should hold. We show that in this
framework Regge behaviour of the structure functions obtained with the hard
pomeron ansatz corresponds to a scaling behaviour of the matrix elements in the
effective theory where the intercept of the hard pomeron appears as a critical
index. Explicit expressions for various analytic continuations of structure
functions and matrix elements are given as well as path integral
representations for the matrix elements in the effective theory. Our aim is to
provide a framework for truely nonperturbative calculations of structure
functions at small x for arbitrary Q^2
