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Letters in Mathematical Physics

, Volume 92, Issue 2, pp 109–124 | Cite as

A Two-Dimensional Analogue of the Luttinger Model

  • Edwin Langmann
Article

Abstract

We present a fermion model that is, as we suggest, a natural 2D analogue of the Luttinger model. We derive this model as a partial continuum limit of a 2D spinless lattice fermion system with local interactions and away from half filling. In this derivation, we use certain approximations that we motivate by physical arguments. We also present mathematical results that allow an exact treatment of parts of the degrees of freedom of this model by bosonization, and we propose to treat the remaining degrees of freedom by mean field theory.

Mathematics Subject Classification (2000)

81Q80 81T25 81T27 

Keywords

lattice fermions quantum field theory in 2+1 dimensions bosonization 

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Copyright information

© Springer 2010

Authors and Affiliations

  1. 1.Theoretical Physics, KTHStockholmSweden

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