CLASSICAL OPEN STRING MODELS IN 4-DIMENSIONAL MINKOWSKI SPACETIME

Classical bosonic open string models in four-dimensional Minkowski spa cetime are discussed. Special attention is paid to the choice of edge conditions, which can follow consistently from the action principle. W e consider Lagrangians that can depend on second order derivatives of world sheet coordinates. A revised interpretation of the variational p roblem for such string theories is given. We derive a general form of a boundary term that can be added to the open string action to control edge conditions and modify conservation laws. An extended boundary pr oblem for minimal surfaces is examined. Following the treatment of thi s model in the geometric approach, we obtain that classical open strin g states correspond to solutions of a complex Liouville equation. In c ontrast with the Nambu-Goto case, the Liouville potential is finite an d constant at world sheet boundaries. The phase part of the potential defines topological sectors of solutions.