Geodesic
Radiative corrections to the electron mass operator in the two-dimensional approximation of quantum electrodynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 38 (1979) no. 2, pp. 195-200

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A study is made into the asymptotic behavior of the diagrams that contribute in fourth order to the mass operator $M$ in a strong magnetic field $B$ in the formal limit $B\to\infty$. The principal term of $M$ increases in proportion to the first power of the field, and comparison with the contribution from the second-order diagrams gives an upper bound on the strength of the field of the form $(\alpha\xi/\ln^2\xi)\sim 1$, where $\xi=B/B_0$, $B_0=m^2/e=4.41\cdot 10^{13}$ G. In stronger fields, the perturbation series diverges. 
@article{TMF_1979_38_2_a5,
     author = {Yu. M. Loskutov and V. V. Skobelev},
     title = {Radiative corrections to the electron mass operator in the two-dimensional approximation of quantum electrodynamics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {195--200},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_38_2_a5/}
}
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Yu. M. Loskutov; V. V. Skobelev. Radiative corrections to the electron mass operator in the two-dimensional approximation of quantum electrodynamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 38 (1979) no. 2, pp. 195-200. http://geodesic.mathdoc.fr/item/TMF_1979_38_2_a5/