Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories

TL;DR

This paper demonstrates a duality in quantum field theories on R^d that relates noncommutativity to non-trivial statistics through twisting, using quantum group methods and braided quantum field theory.

Contribution

It introduces a framework connecting noncommutative and ordinary quantum field theories via twisting, revealing their equivalence and exchanging properties like commutativity and statistics.

Findings

Established a duality between noncommutative and ordinary QFTs.

Extended twisting to an equivalence in braided quantum field theory.

Showed the same duality applies to the noncommutative torus.

Abstract

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.