Landau levels via Jordan superalgebras

TL;DR

This paper demonstrates how Jordan superalgebras offer a concise framework for describing quantum systems with superconformal symmetry, specifically in Landau levels and related models.

Contribution

It introduces the use of Jordan superalgebras to formulate superconformal symmetries in quantum Landau level problems, connecting algebraic structures to physical models.

Findings

Jordan superalgebras describe superconformal symmetries in Landau levels.

The Tits-Kantor-Koecher correspondence links algebraic structures to quantum models.

Extended superconformal algebras are reconstructed using 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.