Spin-Hall effect with quantum group symmetry

Abstract

We construct a model of spin-Hall effect on a noncommutative 4 sphere with isospin degrees of freedom (coming from a noncommutative instanton) and invariance under a quantum orthogonal group. The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ground state; there are both integer and fractional excitations. Similar models exist on higher dimensional noncommutative spheres and noncommutative projective spaces.Comment: v2: 14 pages, latex. Several changes and additional material; two extra sections added. To appear in LMP. Dedicated to Rafael Sorkin with friendship and respec