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.

v2: 14 pages, latex. Several changes and additional material; two extra sections added. To appear in LMP. Dedicated to Rafael Sorkin with friendship and respect

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Cited by in corpus (6)

• Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
• Gauged Laplacians on quantum Hopf bundles
• Noncommutative instantons from twisted conformal symmetries
• Supersymmetric Chern-Simons Theory and Supersymmetric Quantum Hall Liquid
• Braided Hopf algebras and gauge transformations II: $\ast$-structures and examples
• SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry