Landau Level Quantization on the Sphere

TL;DR

This paper introduces a novel formalism for Landau level quantization on the sphere using two mutually commuting SU(2) algebras, extending the well-known planar case.

Contribution

It proposes a new algebraic framework for Landau levels on the sphere, replacing the traditional ladder algebra approach with SU(2) algebras.

Findings

Establishes a formal analogy between planar and spherical Landau levels.

Demonstrates the mathematical consistency of the SU(2) algebra approach.

Provides a foundation for further studies of quantum Hall effects on curved surfaces.

Abstract

It is well established that the Hilbert space for charged particles in a plane subject to a uniform magnetic field can be described by two mutually commuting ladder algebras. We propose a similar formalism for Landau level quantization involving two mutually commuting SU(2) algebras.