Non-commutativity from exact renormalization group dualities

TL;DR

This paper constructs dualities via the exact renormalization group approach and shows that spatial non-commutativity can emerge as a duality in quantum Hall systems, linking commutative and non-commutative models through coarse graining.

Contribution

It introduces a novel method to derive non-commutativity as a duality using the exact renormalization group in a quantum mechanical setting.

Findings

Duality between commutative and non-commutative quantum Hall systems established.

Non-commutativity emerges as a coarse graining transformation.

Exact duality links degrees of freedom in different frameworks.

Abstract

Here we demonstrate, firstly, the construction of dualities using the exact renormalization group approach and, secondly, that spatial non-commutativity can emerge as such a duality. This is done in a simple quantum mechanical setting that establishes an exact duality between the commutative and non-commutative quantum Hall systems with harmonic interactions. It is also demonstrated that this link can be understood as a blocking (coarse graining) transformation in time that relates commutative and non-commutative degrees of freedom.