Operator construction of ghost g-vacuum, handle operator and BRST-invariant multiloop amplitude of the bosonic string

Applying the Feynman-like rules in the operator formalism with bosonized bc-ghost, we construct the g-loop, N-string vertex out of three-string vertices and propagators. The measure factor is analyzed in detail. It is shown that a part of the ghost contribution can be represented by using g 2-differential cand Riemann constants. The resulting measure factor is represented by the ghost g-vacuum with the b-ghost insertion accompanied by a contour integration. This contour integration can be performed explicitly in the one-loop case, in which we reproduce the well-known formula of the one-loop N-tachyon amplitude.