Unified approach to strings and vortices with soliton solutions

A classical relativistic theory of one-dimensional extended objects interacting through a massless scalar field, of which they are in turn the source, is constructed. In the no-coupling limit, the string model is recovered. In another limit, the system that describes nonrelativistic vortex motion in a superfluid is obtained. The diverging self-interaction of these objects is shown to be regularizable through a renormalization of the slope of the Regge trajectories. Motion in an external field is studied in some detail and leads to a system of coupled nonlinear equations that generalizes the sine-Gordon system. Solitary wave solutions to these equations are obtained and a natural geometric interpretation to the associated linear equations of the inverse scattering method is given.