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In order to investigate whether space coordinates are intrinsically noncommutative, we make use of the Hall effect on the two-dimensional plane. We calculate the Hall conductivity in such a way that the noncommutative U(1) gauge invariance is manifest. We find that the noncommutativity parameter theta does not appear in the Hall conductivity itself, but the particle number density of electron depends on theta. We point out that the peak of particle number density differs from that of the charge density.
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 val
A semiclassical constrained Hamiltonian system which was established to study dynamical systems of matrix valued non-Abelian gauge fields is employed to formulate spin Hall effect in noncommuting coordinates at the first order in the constant noncomm
We discuss the quantum Hall effect on a single-layer graphene in the framework of noncommutative (NC) phase space. We find it induces a shift in the Hall resistivity. Furthermore, comparison with experimental data reveals an upper bound on the magnit
When phase space coordinates are noncommutative, especially including arbitrarily noncommutative momenta, the Hall effect is reinvestigated. A minimally gauge-invariant coupling of electromagnetic field is introduced by making use of Faddeev-Jackiw f
We study a system of electrons moving on a noncommutative plane in the presence of an external magnetic field which is perpendicular to this plane. For generality we assume that the coordinates and the momenta are both noncommutative. We make a trans