Geodesic
QED${}_{2+1}$ radiation effects in a strong magnetic field
Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 3, pp. 412-423

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We develop the eigenfunction method for the Dirac operator in a background magnetic field in the $(2+1)$-dimensional quantum electrodynamics (QED${}_{2+1}$). In the eigenfunction representation, we find the exact solutions and the Green's functions of the Dirac equation in a strong constant homogeneous magnetic field in $2+1$ dimensions. In the one-loop QED${}_{2+1}$ approximation, we derive the effective Lagrangian, the density of vacuum fermions induced by the field, and the electron mass operator in a homogeneous background magnetic field. 
@article{TMF_1999_121_3_a4,
     author = {V. R. Khalilov},
     title = {QED${}_{2+1}$ radiation effects in a strong magnetic field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {412--423},
     publisher = {mathdoc},
     volume = {121},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a4/}
}
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V. R. Khalilov. QED${}_{2+1}$ radiation effects in a strong magnetic field. Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 3, pp. 412-423. http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a4/