The Luttinger-Schwinger Model

Details The Luttinger-Schwinger Model The Luttinger-Schwinger Model

1996-09-26

arxiv.org/abs/hep-th/9609206v2

Annals Phys. 253 (1997) 310-331

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, Latex, to appear in Annals of Physics, download problems fixed

Scientific paper

10.1006/aphy.1996.5628

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. 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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