  We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean
4-space by use of a linear map of Weingarten type. We find a geometrically
determined moving frame field at each point of the surface and obtain a system
of geometric functions. We prove a fundamental existence and uniqueness theorem
in terms of these functions. On any Lorentz surface with parallel normalized
mean curvature vector field we introduce special geometric (canonical)
parameters and prove that any such surface is determined up to a rigid motion
by three invariant functions satisfying three natural partial differential
equations. In this way we minimize the number of functions and the number of
partial differential equations determining the surface, which solves the
Lund-Regge problem for this class of surfaces.
