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Geometric construction of the Quantum Hall Effect in all even dimensions

Guowu Meng
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Abstract

The Quantum Hall Effects in all even dimensions are uniformly constructed. Contrary to some recent accounts in the literature, the existence of Quantum Hall Effects does not {\it crucially} depend on the existence of division algebras. For QHE on flat space of even dimensions, both the Hamiltonians and the ground state wave-functions for a single particle are explicitly described. This explicit description immediately tells us that QHE on a higher even dimensional flat space shares the common features such as incompressibility with QHE on plane.

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Guowu Meng. 2003-08-27. Geometric construction of the Quantum Hall Effect in all even dimensions. https://doi.org/10.1088/0305-4470%2F36%2F36%2F301

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