Bethe-Salpeter approach for relativistic positronium in a strong magnetic field

Shabad, A. E.; Усов, В. В.

doi:10.1103/physrevd.73.125021

Cited by 32 publications

(12 citation statements)

References 54 publications

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“…therein). Similar in essence effects are expected to come out also both in 2+1 D (planar graphene-based hetero-structures [14][15][16][17][18][19][20][21]) and in 1+1 D (one-dimensional "hydrogen ion" [22][23][24][25][26][27][28][29]).…”

Section: Introductionmentioning

confidence: 68%

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system II. Vacuum energy

Davydov

Sveshnikov

Voronina

2018

Int. J. Mod. Phys. A

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Non-perturbative vacuum polarization effects are explored for a supercritical Dirac-Coulomb system with Z > Zcr,1 in 2+1 D, based on the original combination of analytical methods, computer algebra and numerical calculations, proposed recently in Refs.[1]- [3]. Both the vacuum charge density ρV P ( r) and vacuum energy EV P are considered. Due to a lot of details of calculation the whole work is divided into two parts I and II. Taking account of results, obtained in the part I [4] for ρV P , in the present part II the evaluation of the vacuum energy EV P is investigated with emphasis on the renormalization and convergence of the partial expansion for EV P . It is shown that the renormalization via fermionic loop turns out to be the universal tool, which removes the divergence of the theory both in the purely perturbative and essentially non-perturbative regimes of the vacuum polarization. The main result of calculation is that for a wide range of the system parameters in the overcritical region EV P turns out to be a rapidly decreasing function ∼ −η ef f Z 3 /R with η ef f > 0 and R being the size of the external Coulomb source. To the end the similarity in calculations of EV P in 2+1 and 3+1 D is discussed, and qualitative arguments are presented in favor of the possibility for complete screening of the classical electrostatic energy of the Coulomb source by the vacuum polarization effects for Z Zcr,1 in 3+1 D.

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Section: Introductionmentioning

confidence: 68%

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system II. Vacuum energy

Davydov

Sveshnikov

Voronina

2018

Int. J. Mod. Phys. A

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“…where U ρ,σ (x),Û ρ,σ (x) = M ρ,σ (x) or W ρ,σ (x), the prime stands for the derivative with respect to the argument, and the explicit form of TrG mj (r, r; iy), which is given in (24), one obtains R1 0 r dr TrG mj (r, r; iy)…”

Section: Appendix A: the Uehling Potential In 2+1 Dmentioning

confidence: 99%

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system I. Vacuum charge density

Davydov

Sveshnikov

Voronina

2018

Int. J. Mod. Phys. A

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Based on the original combination of analytical methods, computer algebra tools and numerical calculations, proposed recently in Refs.[1]-[3], the non-perturbative vacuum polarization effects in the 2+1 D supercritical Dirac-Coulomb system with Z > Zcr,1 are explored. Both the vacuum charge density ρV P ( r) and vacuum energy EV P are considered. The main result of the work is that in the overcritical region EV P turns out to be a rapidly decreasing function ∼ −η ef f Z 3 /R with η ef f > 0 and R being the size of the external Coulomb source. Due to a lot of details of calculation the whole work is divided into two parts I and II. In the present part I we consider the evaluation and behavior of the vacuum density ρV P , which further is used in the part II for evaluation of the vacuum energy, with emphasis on the renormalization, convergence of the partial expansion for ρV P and behavior of the integral induced charge QV P in the overcritical region.

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“…Going beyond the LLL approximation is an ambitious task (see, e.g. (Shabad & Usov, 2006)) which will be left as a subject of our future research.…”

Section: Resultsmentioning

confidence: 99%

Magnetoexciton Binding Energy in Graphene Bilayers

Koinov¹

2011

Physics and Applications of Graphene - Theory

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Bethe-Salpeter approach for relativistic positronium in a strong magnetic field

Cited by 32 publications

References 54 publications

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system II. Vacuum energy

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system II. Vacuum energy

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system I. Vacuum charge density

Magnetoexciton Binding Energy in Graphene Bilayers

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