The action-angle variables for the massless relativistic string in 1+1 dimensions

Abstract

In this paper the Poisson bracket algebra for the open massless relativistic string in the one-space- and one-time-dimensional case is considered. In order to characterize the orbit of the system the directrix function, i.e., the orbit of one of the endpoints of the string, is used. It turns out that the Poisson bracket algebra is of a very simple form in terms of the parameters of the directrix function. We use these results to construct action-angle variables for the general motion of the string. The variables are different for different Lorentz frames, with a continuous dependence. The action-angle variables of the center-of-mass frame and of the light-cone frames are of particular interest with respect to the simplicity of the Poincaré generators and the physical interpretation. For the light-cone frame variables the equivalence to a set of indistinguishable oscillators is shown, for which an excitation corresponds to an instantaneous momentum transfer to an endpoint of the string.