Abstract

The open Nambu string is revisited in the spirit of an early approach by Rohrlich. Strictly timelike motions only are considered. The proper-time of the center-of-mass is taken as preferred parameter. We propose a canonical formalism in terms of a countable infinity of variables, among them the modes. But the barycentric coordinates have noncommuting components, which makes possible a consistent quantization (in any dimension, four in particular) within the framework of a transverse space of states. If a maximal number of modes is further fixed, a transverse Hilbert space emerges, where spacetime displacements preserve the (positive-definite) scalar product