  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.
