Non-commuting coordinates in vortex dynamics and in the Hall effect, related to "exotic" Galilean symmetry

TL;DR

This paper explores vortex dynamics and the Hall effect through a model with non-commuting coordinates derived from an exotic Galilean symmetry, linking superfluid and superconductor behaviors to quantum Hall ground states.

Contribution

It introduces a classical model with non-commuting coordinates based on exotic Galilean symmetry, connecting vortex dynamics to fractional quantum Hall physics.

Findings

Model reproduces vortex behavior in superfluid and superconductor films.

Links classical vortex dynamics to quantum Hall ground states.

Highlights the role of exotic Galilean symmetry in condensed matter systems.

Abstract

Vortex dynamics in a thin superfluid ${}^4$He film as well as in a type II superconductor is described by the classical counterpart of the model advocated by Peierls, and used for deriving the ground states of the Fractional Quantum Hall Effect. The model has non-commuting coordinates, and is obtained by reduction from a particle associated with the ``exotic'' extension of the planar Galilei group.