Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-11-29
J.Math.Phys. 43 (2002) 4592; Erratum-ibid. 45 (2004) 827
Physics
High Energy Physics
High Energy Physics - Theory
13 pages. Some references added
Scientific paper
We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained. We derive the electric current whose expectation value gives the Hall effect in terms of an effective magnetic field. We present a receipt to find the action which can be utilized in path integrals for noncommuting coordinates. In terms of this action we calculate the related Aharonov--Bohm phase and show that it also yields the same effective magnetic field. When magnetic field is strong enough this phase becomes independent of magnetic field. Measurement of it may give some hints on spatial noncommutativity. The noncommutativity parameter \theta can be tuned such that electrons moving in noncommutative coordinates are interpreted as either leading to the fractional quantum Hall effect or composite fermions in the usual coordinates.
Dayi Omer F.
Jellal Ahmed
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