Interfaces of relativistic membranes and Neumann's triangle

Abstract

We examine, from a geometrical point of view, the dynamics of relativistic extended objects joined at some interface. Using simple variational techniques, we obtain the equations of motion for these objects, together with a set of dynamical boundary conditions, that express the feedback of the motion of the interface on the joining membranes. These conditions reduce, in a particular limit, to a relativistic dynamical generalization of Neumann's triangle. For simplicity, we restrict our attention to Dirac-Nambu-Goto extended objects.