96-447 H. Grosse, E. Langmann, E. Raschhofer

The Luttinger-Schwinger Model (57K, Latex) Sep 26, 96

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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.

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