SCATTERING-AMPLITUDES AND LOOP CORRECTIONS IN COLLECTIVE STRING FIELD-THEORY

Using collective field theory we compute the scattering of one-dimensional strings. The amplitude is determined and seen to have a contribution from the tachyon as well as from an infinite sequence of discrete states. It is not proportional to the length of the space and is finite. We then consider the issue of higher-loop corrections in collective string field theory. The two-loop diagrams are evaluated and the correction to the ground-state energy is found to be in exact agreement with the finite value obtained previously from matrix model calculations. We also point to the origin of the large-order behavior in collective field theory.