Higher-dimensional Dunkl–Pauli equation with spin and magnetic fields

Develop and analyze a higher-dimensional generalization of the Dunkl–Pauli equation in an external magnetic field that determines how spin degrees of freedom and the tensorial magnetic field affect separability and the underlying algebraic structure.

Background

The paper treats a two-dimensional spin-1/2 Dunkl–Pauli equation in a uniform magnetic field and relies on two-dimensional separation and radial $\mathfrak{su}(1,1)$ methods. Although scalar Dunkl systems are established in arbitrary dimensions, extending the spin-dependent magnetic problem is not immediate.

The authors identify the unresolved technical issues as the effects of spin and the tensorial nature of the magnetic field on separability and on the algebraic structure. A careful higher-dimensional formulation is therefore left for future investigation.