Particle theories with minimum observable length and open string theory

We investigate a class of particle theories that have minimum observable length. Among them we find the theory equivalent to the open bosonic string theory. For this theory, starting from a reparametrization invariant and non-local action with respect to a world-line parameter, we derive the Virasoro constraint and the Veneziano amplitude. The possible relation to other attempts to introduce a functiontal length scale into particle theory is also discussed. (orig.)