  Semiclassical approach has been developed for the one-dimensional interacting
fermion systems. Starting from the incommensurate spin density wave (SDW) mean
field state for the repulsive Hubbard model in 1D, the non-Abelian bosonized
Lagrangian describing the spin-charge separation is obtained. The Berry phase
term is derived from the chiral anomaly, and we obtain the massless
Tomonaga-Luttinger liquid in the single chain case while the spin gap opens in
the double-chain system. This approach offers a new method to identify the
strong-coupling fixed point, and its relation to the Abelian bosonization
formalism is discussed on the spin gap state. The generalization to higher
dimensions is also discussed.
