Degeneracy of Landau Level and Quantum Group SL_q(2)

TL;DR

This paper reveals that the degeneracy of Landau levels in the quantum Landau problem is governed by the quantum group symmetry $ sl_{q}(2) $, linking degeneracy to the dimension of its irreducible cyclic representations.

Contribution

It demonstrates the presence of quantum group symmetry in the Landau problem and connects degeneracy to the representation theory of $ sl_{q}(2) $.

Findings

Degeneracy of Landau levels is finite under periodic boundary conditions.

Degeneracy equals the dimension of irreducible cyclic representations of $ sl_{q}(2)$.

Quantum group symmetry governs Landau level degeneracy.

Abstract

We show that there is a kind of quantum group symmetry $ sl_{q}(2) $ in the usual Landau problem and it is this quantum group symmetry that governs the degeneracy of Landau levels. We find that under the periodic boundary condition, the degree of degeneracy of Landau levels is finite, and it just equals the dimension of the irreducible cyclic representation of the quantum group $ sl_{q}(2) $.