  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 \delta
m_{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 :\delta m_{LLL} ->
(\alpha/2)\sqrt{pi/2}sqrt{\hbar|e|B/c^2}; 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.
