Making the massless string massive

Abstract

We investigate the possibility of associating a finite rest mass density with the relativistic string at the classical level. We choose a modification of the massless Lagrangian which reduces in the non-relativistic limit to the usual non-relativistic string. After studying some simple classical motions of this system, we quantize the massive string in a similar way to the massless case. The Regge trajectories are linear as in the massless case, but their intercepts are shifted downward from unity by an amount proportional to the square of the rest mass density parameter. Our naive quantization procedure is covariant only in 25 space-time dimensions. However, we are able to use the extra degree of freedom implicit in the mass density to modify the Lorentz generators so that covariance is maintained for any dimension less than 25. We envisage hadronic interactions to be introduced through the breaking and joining of strings, as in the massless case, and we discuss the problems associated with the construction of covariant amplitudes when D < 25.