Landau levels via Jordan superalgebras

Abstract

The goal of this note is to show that Jordan algebras and superalgebras provide an elegant and concise language for formulating quantum mechanical problems with inherent (super)conformal symmetry. The superconformal symmetries of the quantum MICZ-Kepler model and its dual oscillator realization in ${\mathbb{R}}^2$ are reviewed through the lens of the Tits-Kantor-Koecher correspondence: Kaplansky $\mathfrak{J}{\mathbb{R}}^{1|2}$ and Exceptional $\mathfrak{J}{F}^{6|4}$ Jordan superalgebras provide a natural framework for reconstructing (variously extended) superconformal algebras hidden in the Landau levels of an electron in an external magnetic field.

13 pages, contribution to the XVI International Workshop "Lie Theory and Its Applications in Physics" (Varna,Bulgaria, June 2025)