  In this paper we consider some analytic properties of the high--energy
quark--quark scattering amplitude, which, as is well known, can be described by
the expectation value of two lightlike Wilson lines, running along the
classical trajectories of the two colliding particles. We shall prove that the
expectation value of two infinite Wilson lines, forming a certain hyperbolic
angle in Minkowski space--time, and the expectation value of two infinite
Euclidean Wilson lines, forming a certain angle in Euclidean four--space, are
connected by an analytic continuation in the angular variables. This could open
the possibility of evaluating the high--energy scattering amplitude directly on
the lattice or using the stochastic vacuum model. The Abelian case (QED) is
also discussed.
