Landau levels from noncommutative U (1) ∗ gauge theory in κ -Minkowski space-time

Abstract

Motivated by physics of the Lowest Landau Level and the Quantum Hall Effect, we investigate motion of an electron in a constant background magnetic field in the κ-Minkowski space-time. Starting from an action invariant under the noncommutative U(1) gauge transformations, we obtain the κ-deformed Dirac equation. Using the perturbative approach, we calculate noncommutative corrections to energy levels, mass and the gyromagnetic ratio up to the first order in the deformation parameter a = 1/ κ.