Quantum Hall effect in higher dimensions Original Research Article

Following recent work on the quantum Hall effect on S4, we solve the Landau problem on the complex projective spaces CPk and discuss quantum Hall states for such spaces. Unlike the case of S4, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of CP2 in some detail considering both Abelian and nonAbelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of CP3 is related to the case of S4.