H. Grosse, E. Langmann, E. Raschhofer
The Luttinger-Schwinger Model
(57K, Latex)
ABSTRACT. We study the Luttinger--Schwinger model, i.e. the (1+1) dimensional model
of massless Dirac fermions with a non-local 4--point interaction coupled to
a U(1)-gauge field. We work within the Hamiltonian framework on
the cylinder, and construct the field operators and observables
as well--defined operators on the physical Hilbert space. The complete
solution of the model is found using the boson--fermion correspondence, and
the formalism for calculating all gauge invariant Green functions is
provided. We discuss the role of anomalies and show how the existence of
large gauge transformations implies a fermion condensate in all physical
states. The meaning of regularization and renormalization in our
well--defined Hilbert space setting is discussed. We illustrate the latter by
performing the limit to the Thirring--Schwinger model where the
interaction becomes local.