Polyakov path integrals with ghosts: Closed strings and one-loop amplitudes

A technique for evaluating the Polyakov path integral with ghosts, previously applied by us to the bosonic open-string propagator, is used to obtain the bosonic closed-string propagator. One-loop vacuum amplitudes for oriented and unoriented open and closed strings are computed using these results, and aspects of the 'sewing rules' needed to construct string field theory from the path integral are discussed. (orig.)