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Landau levels from noncommutative $U {(1)}_{⋆}$ gauge theory in $κ$ -Minkowski space-time

Marija Dimitrijević Ćirić

Faculty of Physics, University of Belgrade, Studentski trg 12, 11000 Belgrade, Serbia

E-mail Address: dmarija@ipb.ac.rs

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and

Nikola Konjik

Faculty of Physics, University of Belgrade, Studentski trg 12, 11000 Belgrade, Serbia

E-mail Address: konjik@ipb.ac.rs

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https://doi.org/10.1142/S0219887818501414Cited by:0 (Source: Crossref)

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 $a = \frac{1}{κ}$ .

Keywords:

AMSC: 81T75, 70S15, 81V70

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