Non-commutativity effects in the Dirac equation in crossed electric and magnetic fields

Article Type

Research Article

Publication Title



In this paper we present exact solutions of the Dirac equation on the non-commutative plane in the presence of crossed electric and magnetic fields. In the standard commutative plane such a system is known to exhibit contraction of Landau levels when the electric field approaches a critical value. In the present case we find exact solutions in terms of the non-commutative parameters η (momentum non-commutativity) and θ (coordinate non-commutativity) and provide an explicit expression for the Landau levels. We show that non-commutativity preserves the collapse of the spectrum. We provide a dual description of the system: i) one in which at a given electric field the magnetic field is varied and the other ii) in which at a given magnetic field the electric field is varied. In the former case we find that momentum non-commutativity (η) splits the critical magnetic field into two critical fields while coordinates non-commutativity (θ) gives rise to two additional critical points not at all present in the commutative scenario.



Publication Date



All Open Access, Green

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