1-Loop mass generation by a constant external magnetic field for an electron propagating in a thin medium

Abstract : The 1-loop self-energy of a Dirac electron of mass m propagating in a thin medium simulating graphene in an external magnetic field B is investigated in Quantum Field Theory. Equivalence is shown with the so-called reduced QED 3+1 on a 2-brane. Schwinger-like methods are used to calculate the self-mass δm LLL of the electron when it lies in the lowest Landau level. Unlike in standard QED 3+1 , it does not vanish at the limit m → 0 : δm LLL m→0 → α 2 π 2 |e|B c 2 (with α = e 2 4πc); all Landau levels of the virtual electron are taken into account and on mass-shell renormalization conditions are implemented. Restricting to the sole lowest Landau level of the virtual electron is explicitly shown to be inadequate. Resummations at higher orders lie beyond the scope of this work.
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International Journal of Modern Physics B, World Scientific Publishing, 2018, 〈10.1142/S021797921850114X〉
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Bruno Machet. 1-Loop mass generation by a constant external magnetic field for an electron propagating in a thin medium. International Journal of Modern Physics B, World Scientific Publishing, 2018, 〈10.1142/S021797921850114X〉. 〈hal-01723541〉

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