Classes of f-Deformed Landau Operators: Nonlinear Noncommutative Coordinates from Algebraic Representations

TL;DR

This paper explores new operator-dependent noncommutative geometries in superspace related to f-deformed Landau operators, using algebraic representations to define different coordinate algebras and a reduced model with N=2 superalgebra.

Contribution

It introduces novel noncommutative coordinate algebras derived from algebraic representations of f-deformed Landau operators in superspace, including a reduced model with N=2 superalgebra.

Findings

Defined new NC coordinate algebras using unitary representations.

Connected algebraic structures to nonlinear quantum Hall effects.

Presented a reduced model with underlying N=2 superalgebra.

Abstract

We consider, in a superspace, new operator dependent noncommutative (NC) geometries of the nonlinear quantum Hall limit related to classes of f-deformed Landau operators in the spherical harmonic well. Different NC coordinate algebras are determined using unitary representation spaces of Fock-Heisenberg tensored algebras and of the Schwinger-Fock realisation of the su(1,1) Lie algebra. A reduced model allowing an underlying N=2 superalgebra is also discussed.