Ulm 2004 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 3: Strings und Quantentheorie in externen Feldern

MP 3.5: Fachvortrag

Dienstag, 16. März 2004, 15:40–16:05, H 22

Exact solution of a 1D many-body system with momentum dependent interactions — •Cornelius Paufler¹, Harald Grosse² und Edwin Langmann¹ — ¹Kungl Tekniska Högskolan, AlbaNova - SCFAB, SE-10691 Stockholm, Sweden — ²Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria

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 can be obtained as the non-relativistic limit of the massive Thirring model. This fermion model can be solved exactly by mapping it to the 1D boson gas with inverse coupling constant which we interpret as the non-relativistic limit of the duality between the massive Thirring model and the quantum sine-Gordon model. We demonstrate that the generalized model with distinguishable particles remains exactly solvable by a Bethe ansatz. Our solution provides a generalization of the above mentioned boson-fermion duality to particles with arbitrary exchange statistics characterized by any irreducible representation of the permutation group.