Dortmund 2006 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 7: Symmetrien, integrable Systeme und Nichtkomm. Geometrie

MP 7.2: Talk

Wednesday, March 29, 2006, 17:30–18:00, P1-02-111

Diagonalizing 1-d interacing particle systems — •Heiner Kohler — Universität Heidelberg

We present a new first–quantization approach to construct wave functions for a certain class of exactly solvable one–dimensional interacting many–body systems. This class comprises the Calogero-Moser-Sutherland Hamiltonians but also particles with δ interaction. We construct coordinate representations of creation and anihilation operators for the elementary exitations and thereby essentially diagonalize the complete many body Hamiltonian. Our construction, alternative to the Bethe Ansatz, is in principle not restricted to local interactions. It is especially well suited to construct states representing particle hole excitations with respect to the many body ground state. It provides a different aspect on the underlying integrable structure of the models under consideration. A group theoretical interpretation is also given.