Hall effect in Noncommutative spaces

TL;DR

This paper explores the Hall effect in noncommutative spaces, revealing that while the Hall conductivity remains unaffected by noncommutativity, the particle number density does depend on the noncommutative parameter theta.

Contribution

It demonstrates how noncommutative geometry influences particle density without altering the Hall conductivity, maintaining gauge invariance.

Findings

Hall conductivity is independent of noncommutative parameter theta.

Particle number density depends on theta, affecting its peak position.

Charge density and particle number density peaks differ in noncommutative spaces.

Abstract

In order to investigate whether space coordinates are intrinsically noncommutative, we make use of the Hall effect on the two-dimensional plane. We calculate the Hall conductivity in such a way that the noncommutative U(1) gauge invariance is manifest. We find that the noncommutativity parameter theta does not appear in the Hall conductivity itself, but the particle number density of electron depends on theta. We point out that the peak of particle number density differs from that of the charge density.