Quantum Hall effect in higher dimensions

Karabali, Dimitra; Nair, V.P.

doi:10.1016/S0550-3213(02)00634-X

Quantum Hall effect in higher dimensions

Dimitra Karabali
(
- Lehman Coll. and
- CUNY, Graduate School - U. Ctr.
)
,
V.P. Nair
(
- City Coll., N.Y. and
- CUNY, Graduate School - U. Ctr.
)

Mar, 2002

15 pages

Published in:

Nucl.Phys.B 641 (2002) 533-546

e-Print:

hep-th/0203264 [hep-th]

DOI:

10.1016/S0550-3213(02)00634-X

Report number:

CCNY-HEP-02-03

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Abstract:

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

.

Hall effect
space: CP(N)
background field
gauge field theory: U(1)
gauge field theory: SU(2)
wave function
charged particle: nonrelativistic

References(14)

Figures(0)

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