Exact solution of a 1D many-body system with momentum dependent interactions

Details Exact solution of a 1D many-body system with momentum dependent interactions Exact solution of a 1D many-body system with momentum dependent interactions

2004-01-05

arxiv.org/abs/math-ph/0401003v2

J.Phys.A37:4579,2004

Physics

Mathematical Physics

12 pages; mistake corrected changing one of our conclusions: the generalized model with distinguishable particles is not exact

Scientific paper

10.1088/0305-4470/37/16/008

We discuss a 1D many-body model of distinguishable particles with local, momentum dependent two-body interactions. We show that the restriction of this model to fermions corresponds to the non-relativistic limit of the massive Thirring model. This fermion model can be solved exactly by a mapping to the 1D boson gas with inverse coupling constant. We provide evidence that this mapping is the non-relativistic limit of the duality between the massive Thirring model and the quantum sine-Gordon model. We also investigate the question if the generalization of this model to distinguishable particles is exactly solvable by the coordinate Bethe ansatz and find that this is not the case.

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