Modified models of a free boson string and their solutions

Abstract

In this paper we consider the modified models of a free boson string and examine their dynamics. Modified models of the boson string are investigated from the point of view of the second order formalism (the Polyakov action). The motion of the free string propagates in Minkowski space-time. The internal geometry of the free boson string is described by the metric hαβ having the signature of Minkowski. The classical string trajectory is described by the function Xμ. The introduction of the function K and the potential V(Xμ) into the action of the boson string allows us to find new approaches to solving the problem of the boson string dynamics. For these modified models of the boson string the equations of motion are found. The equations of motion are obtained by varying the action with respect to Xμ. The energy-momentum tensor for considered models of the free boson string is calculated. Constraint conditions are obtained for all types of modified boson string models. It is proved that constraint conditions are satisfied for each considered modified model of the boson string. Solutions of the equations of motion for each modified boson string model are also considered and obtained. String’s world sheet has been built for these solutions. It is shown that all solutions for these models satisfy the equations of motion and the constraint conditions.