Operator approach to bosonic string: Multiloop calculation and b-ghost insertion

We construct the g-loop N-string vertex using the Feynman-like rules in the operator formalism with bosonized bc ghosts. The measure factor is analyzed in detail, which consists of the ghost g vacuum and the contour integration associated with the b-ghost insertion. The general form of the g vacuum is derived using the handle operators. The handle operator is formulated by the geometrical quantities: period matrix, first Abelian integral, prime form, differential, and Riemann constant. Explicit results are given up to two-loop level. The contour integrations associated with the ghost insertions can be performed explicitly in the one-loop case, in which we reproduce the well-known formula of the one-loop N-tachyon amplitude.