A Family of Non-commutative geometries

Details A Family of Non-commutative geometries A Family of Non-commutative geometries

2010-10-21

arxiv.org/abs/1010.4418v1

Mod. Phys. Lett. A26:2213-2221,2011

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, revtex

Scientific paper

10.1142/S0217732311036619

It is shown that the non-commutativity in quantum Hall system may get modified. The self-adjoint extension of the corresponding Hamiltonian leads to a family of non-commutative geometries labeled by the self-adjoint extension parameters. We explicitly perform an exact calculation using a singular interaction and show that, when projected to a certain Landau level, the emergent non-commutative geometries of the projected coordinates belong to a one parameter family. There is a possibility of obtaining the filling fraction of fractional quantum Hall effect by suitably choosing the value of the self-adjoint extension parameter.

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