Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-03-28
Nucl.Phys. B641 (2002) 533-546
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, LaTeX
Scientific paper
10.1016/S0550-3213(02)00634-X
Following recent work on the quantum Hall effect on $S^4$, we solve the Landau problem on the complex projective spaces ${\bf C}P^k$ and discuss quantum Hall states for such spaces. Unlike the case of $S^4$, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of ${\bf C}P^2$ 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 ${\bf C}P^3$ is related to the case of $S^4$.
Karabali Dimitra
Nair V. P.
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