  We show that there is a duality exchanging noncommutativity and non-trivial
statistics for quantum field theory on R^d. Employing methods of quantum
groups, we observe that ordinary and noncommutative R^d are related by
twisting. We extend the twist to an equivalence for quantum field theory using
the framework of braided quantum field theory. The twist exchanges both
commutativity with noncommutativity and ordinary with non-trivial statistics.
The same holds for the noncommutative torus.
