Bosonization of fermions in two-dimensional models

Marian Apostol

J. Sakamoto, a. B. R. Poudel

We present a new bosonization procedure for two-dimensional fermion models in the path integral formulation. We introduce external sources for the fermion currents instead of the auxiliary boson fields used in the conventional procedure. The calculations become much simpler because the external sources do not interact with themselves, while the auxiliary boson fields do, and we can find the equivalent boson models directy. All the formulations are done in Minkowski space-time. The extended Bukhvostov-Lipatov model and the massive Thirring model are discussed here as typical two-dimensional fermion models with current-current-type interactions. The Rothe and Stamatescu model is also discussed, though this is slightly out of the context of bosonization, and the relation of the fermion current in the Heisenberg picture with that in the interaction picture is derived almost straightforwardly. Usually in the operator formalism, this relation is derived using the splitting procedure, which requires detailed calculations. It is expected that we can derive the boson model equivalent to the fermion model with SU(N) symmetry more easily and without any guess work.

Yoshio Kuramoto

Marian Apostol

Jordan's theory of the boson representation of the fermion fields in one dimension is reviewed and generalised to the one-dimensional two-fermion model (TFM). It is shown that an additional constraint (Jordan's commutator) on the fermion fields has been overlooked so far by the theory of the TFM. This supplementary condition requires a particular cut-off procedure which has been little considered in recent times.

Peter Kopietz

Seiju Ami