Non-commutative geometry and exactly solvable systems
Abstract
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.
Cite
@article{arxiv.0710.5859,
title = {Non-commutative geometry and exactly solvable systems},
author = {Edwin Langmann},
journal= {arXiv preprint arXiv:0710.5859},
year = {2008}
}
Comments
Contribution to the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France)