Geodesic
Fermions in strong external fields in $2+1$ and $1+1$ dimensions
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 3, pp. 372-384 Cet article a éte moissonné depuis la source Math-Net.Ru

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The creation of electron-positron pairs from a vacuum by an external Coulomb field is examined within $(2+1)$-dimensional quantum electrodynamics. If the electromagnetic coupling constant exceeds $0.62$ $(Z=85)$, then in a simple model with a finite-size nucleus, the lower electron level crosses the boundary of the negative-energy continuum (i.e., Dirac sea), and a hole (i.e., positively charged fermion) appears in the negative-energy continuum. An equation is obtained that describes the levels of the ground and excited electron states in a strong Coulomb field of the nucleus. The critical nucleus charge is found for a few lowest electron states. The critical charge in $2+1$ dimensions is significantly smaller than in $3+1$ dimensions. The problem is reduced to the case of a bounded Coulomb field in $1+1$ dimensions without a magnetic field. The interaction of a fermion and an external scalar field in $2+1$ and $1+1$ dimensions is investigated. 
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     author = {V. R. Khalilov},
     title = {Fermions in strong external fields in $2+1$ and $1+1$ dimensions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {372--384},
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     volume = {122},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_122_3_a4/}
}
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V. R. Khalilov. Fermions in strong external fields in $2+1$ and $1+1$ dimensions. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 3, pp. 372-384. http://geodesic.mathdoc.fr/item/TMF_2000_122_3_a4/

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