2007/10/31 by Edwin Langmann, E Langmann
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP #msc:81R12 #msc:81R60 #msc:81V70
paper · pdf · doi:10.1088/1742-6596/103/1/012015
published as J.Phys.Conf.Ser.103:012015,2008 · Contribution to the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France)
arxiv created 2007/10/31 · openalex publication_date 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/04
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.