Non-commutative geometry and exactly solvable systems

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Langmann, Edwin
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Abstract
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I present the exact energy eigenstates and eigenvalues of a quantum many-body system of bosons on non-commutative space and in a harmonic oszillator confining potential at the selfdual point. I also argue that this exactly solvable system is a prototype model which provides a generalization of mean field theory taking into account non-trivial correlations which are peculiar to boson systems in two space dimensions and relevant in condensed matter physics. The prologue and epilogue contain a few remarks to relate my main story to recent developments in non-commutative quantum field theory and an addendum to our previous work together with Szabo and Zarembo on this latter subject.
Comment: Contribution to the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France)
Keywords
Mathematical Physics, 81R60, 81R12, 81V70
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