g-Loop vertices for free fermions and bosons

We construct an N-point g-loop vertex for the conformal theory of free fermions of spin with the properly of reproducing the N-point correlation functions of the primary fields of the theory on arbitrary Reimann surfaces. It turns out to be written in terms of the Szegö kernel. The same construction is then performed for free real scalar fields, checking the bosonization rules of the free fermionic theory, by the use of the covariant operatorial formalism.