Behavior of the mass operator in a superstrong magnetic field: Summation of the perturbation theory diagrams

Loskutov, Yu. M.; Скобелев, В. В.

doi:10.1007/bf01037983

Cited by 12 publications

(16 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The exponential factor displays the nonperturbative nature of this result. We note that the double logarithmic asymptotics of the electron selfenergy in a magnetic field in the standard perturbation theory was obtained in earlier papers [16,17].…”

mentioning

confidence: 51%

Chiral symmetry breaking in QED in a magnetic field at finite temperature

Gusynin

Shovkovy

1997

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

mentioning

confidence: 51%

Chiral symmetry breaking in QED in a magnetic field at finite temperature

Gusynin

Shovkovy

1997

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…Then q ′ can be also neglected in the arguments (34). If, contrary to the previous assumption, we admit that…”

Section: B Equation For the Fourier-ritus Transform Of The Bethe-salmentioning

confidence: 99%

“…But we can disregard A 2 as compared with eB(z 2 − t 2 ) to make sure that the integration over dq ′ is restricted to the region close to zero |q| ′ < [eB(z 2 − t 2 )] −1/2 and hence set q ′ = 0 in (34). The contribution of large q ′ is small as before.…”

Section: B Equation For the Fourier-ritus Transform Of The Bethe-salmentioning

confidence: 99%

See 1 more Smart Citation

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

Shabad

Усов

2006

Phys. Rev. D

View full text Add to dashboard Cite

We study the electron-positron system in a strong magnetic field using the differential BetheSalpeter equation in the ladder approximation. We derive the fully relativistic two-dimensional form that the four-dimensional Bethe-Salpeter equation takes in the limit of asymptotically strong constant and homogeneous magnetic field. An ultimate value for the magnetic field is determined, which provides the full compensation of the positronium rest mass by the binding energy in the maximum symmetry state and vanishing of the energy gap separating the electron-positron system from the vacuum. The compensation becomes possible owing to the falling to the center phenomenon that occurs in a strong magnetic field because of the dimensional reduction. The solution of the Bethe-Salpeter equation corresponding to the vanishing energy-momentum of the electron-positron system is obtained.

show abstract

“…Later on, in the papers by Loskutov and Skobelev [2,3] the attempts were performed to calculate the two-loop contribution and to summarize all the manyloop contributions in the same approximation. A correct formula for the electron mass operator in this approximation was obtained recently in the paper [4].…”

mentioning

confidence: 99%

Electron Mass Operator in a Strong Magnetic Field and Dynamical Chiral Symmetry Breaking

Кузнецов

2002

Phys. Rev. Lett.

View full text Add to dashboard Cite

The electron mass operator in a strong magnetic field is calculated. The contribution of higher Landau levels of virtual electrons, along with the ground Landau level, is shown to be essential in the leading log approximation. The effect of the electron dynamical mass generation by a magnetic field is investigated. In a model with N charged fermions, it is shown that some critical number Ncr exists for any value of the electromagnetic coupling constant α, such that the fermion dynamical mass is generated with a doublet splitting for N < Ncr, and the dynamical mass does not arise at all for N > Ncr, thus leaving the chiral symmetry unbroken.PACS numbers: 11.30. Rd, 11.30.Qc, 12.20.Ds Asymptotic properties of the QED diagrams and operators in strong magnetic fields B ≫ B e , B e = m 2 e /e ≃ 4.41 · 10 13 G (e is the elementary charge) are of conceptual interest both from the standpoint of the searches of the perturbation theory applicability borders, and also in view of possible applications in astrophysics and in cosmology of the early Universe. The investigations of this type are being performed by many authors during a rather long time. For example, a history of calculations of the electron mass operator in a strong magnetic field lasts more than 30 years already. However, as we show in this Letter, it is too early to put the final point in the problem.One-loop contribution into the electron mass operator in a strong magnetic field was obtained for the first time by Jancovici [1] in the leading (double) log approximation. Later on, in the papers by Loskutov and Skobelev [2, 3] the attempts were performed to calculate the two-loop contribution and to summarize all the manyloop contributions in the same approximation. A correct formula for the electron mass operator in this approximation was obtained recently in the paper [4]. However, the double log approximation becomes invalid in asymptotically strong magnetic fields [5], because of the crucial influence of the strong magnetic field on the virtual photon polarization operator. This influence provides an appearance of the effective photon mass, m 2 γ = (2α/π)eB, which replaces the electron mass in one of the two logarithms. A correct expression for the electron mass operator in the leading (single) log approximation was obtained recently in our paper [6] by the summation of the rainbow Feynman diagrams, in the form:where m 0 is the electron mass without field, γ E = 0.577 . . . is the Euler constant, α R is the electromagnetic coupling constant renormalized by the fieldHowever, the formula (1) has a restricted area of applicability with respect to the parameter η 0 = α 2π ln eB m 2 0

show abstract

Behavior of the mass operator in a superstrong magnetic field: Summation of the perturbation theory diagrams

Cited by 12 publications

References 2 publications

Chiral symmetry breaking in QED in a magnetic field at finite temperature

Chiral symmetry breaking in QED in a magnetic field at finite temperature

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

Electron Mass Operator in a Strong Magnetic Field and Dynamical Chiral Symmetry Breaking

Contact Info

Product

Resources

About