Abstract

The generating functional of two dimensional BF field theories coupled to fermionic fields and conserved currents is computed in the general case when the base manifold is a genus g compact Riemann surface. The Lagrangian density L = dB boolean AND A is written in terms of a globally defined 1-form A and a multivalued scalar held B. Consistency conditions on the periods of dB have to be imposed. It is shown that there is a nontrivial dependence of the generating functional on the topological restrictions imposed to B. In particular if the periods of the B field are constrained to take values -4 pi n. with n any integer, then the partition Function is independent of the chosen spin structure and may be written as a sum over all the spin structures associated with the fermions even when one started with a fixed spin structure, These results are then applied to the functional bosonization of fermionic fields on higher genus surfaces. A bosonized form of the partition function which takes care of the chosen spin structure is obtained.