A Family of Non-commutative geometries
High Energy Physics - Theory
2011-09-28 v1 Mesoscale and Nanoscale Physics
Abstract
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.
Keywords
Cite
@article{arxiv.1010.4418,
title = {A Family of Non-commutative geometries},
author = {Debabrata Sinha and Pulak Ranjan Giri},
journal= {arXiv preprint arXiv:1010.4418},
year = {2011}
}
Comments
5 pages, revtex