Untwisting noncommutative Rd and the equivalence of quantum field theories Original Research Article

We show that there is a duality exchanging noncommutativity and non-trivial statistics for quantum field theory on Rd. Employing methods of quantum groups, we observe that ordinary and noncommutative Rd 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.