  We consider the generalized chiral $QED_2$ on $S^1$ with a $U(1)$ gauge field
coupled with different charges to both chiral components of a fermionic field.
Using the adiabatic approximation we calculate the Berry phase and the
corresponding ${\rm U}(1)$ connection and curvature for the vacuum and many
particle Fock states. We show that the nonvanishing vacuum Berry phase is
associated with a projective representation of the local gauge symmetry group
and contributes to the effective action of the model.
