Bosonization of current-current interactions

We discuss a generalization of the conventional bosonization procedure to the case of current-current interactions which have a natural representation in terms of current instead of fermion-number-density operators. A consistent bosonization procedure requires a geometrical quantization of the Hamiltonian action of W on its coadjoint orbits. An integrable example of a nontrivial realization of this symmetry is presented by the Calogero-Sutherland model. For an illustrative nonintegrable example we consider transverse gauge interactions and calculate the fermion Green function.