Vertices in the discretized approach to string field theory

We work out in detail an approach to the Witten string field theory based on the discretization of the world-sheet σ coordinate. We consider the string fields as the limit N→∞ of N point functions. The relation with the more conventional approach based on the Fock space is discussed. We also calculate numerically the interaction vertex for various string states. For a string approximated by 600 points the numerical results agree within 0.02% with the predicitons of the dual model. The computational method is very flexible and could find applications where other approaches are technically unsuited. (orig.)