Multiloop correlators and bosonic string amplitudes in the operator formalism

The operator formalism for bosonic free fields on Riemann surfaces is used to determine correlation functions for closed bosonic string vertex operators corresponding to the emission of tachyons, gravitons, antisymmetric tensor fields and dilatons. This is generalized to correlators of a 'vertex generating operator' from which those of arbitrary excited states can be deduced by differentiation. Results are obtained for correlators over arbitrary points of the bosonic universal grassmannian manifold (UGM) and then specialized to Riemann surfaces of arbitrary genus and period matrix. The corresponding string scattering amplitudes can be explicitly written down in genus one, two and three. (orig.)