A Family of Non-commutative geometries

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.

5 pages, revtex

References in corpus (7)

• Interactions and non-commutativity in quantum Hall systems
• Noncommutative oscillator, symmetry and Landau problem
• Quantum Mechanics on Noncommutative Spacetime
• Electron Capture and Scaling Anomaly in Polar Molecules
• Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
• Non-Hermitian quantum mechanics in non-commutative space
• Dipole binding in a cosmic string background due to quantum anomalies