Gauged Laplacians on quantum Hopf bundles

TL;DR

This paper analyzes gauged Laplacian operators on quantum spheres, revealing their spectral properties and potential applications to quantum Hall effect models, with a focus on symmetry and magnetic monopole interactions.

Contribution

It introduces a detailed study of gauged Laplacians on quantum Hopf bundles, including their diagonalization and physical interpretation in quantum magnetic monopole contexts.

Findings

Operators describe excitations on quantum spheres in magnetic fields

Energy spectra are asymmetric under monopole/antimonopole exchange

Potential relevance to quantum Hall effect models

Abstract

We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum sphere' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.