Photon dispersion in a strong magnetic field with positronium formation: Theory

Shabad, A. E.; Усов, В. В.

doi:10.1007/bf00644586

Cited by 47 publications

(90 citation statements)

References 19 publications

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“…Moreover, a conjecture exists [17] that the Feynman rules in the high magnetic field limit may be directly served by two-dimensional (one space + one time) form of electron propagators. As applied to the Bethe-Salpeter equation, the dimensional reduction in high magnetic field was considered in [9,10]. In these references the well-known simultaneous approximation to the Bethe-Salpeter equation taken in the integral form was exploited, appropriate for nonrelativistic treatment of the relative motion of the two charged particles.…”

Section: Two-dimensional Bethe-salpeter Equation For Positron-iummentioning

confidence: 99%

“…(cf the corresponding form of the Coulomb potential in the semi-relativistic treatment of the Bethe-Salpeter equation in [10,11]-the difference between the potentials in [10,11] lies within the accuracy of the adiabatic approximation). The appearance of P 2 1 in the potential determines the energy spectrum dependence upon the momentum of motion of the two-particle system across the magnetic field like in [10], [11], [21].…”

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

confidence: 99%

“…The appearance of P 2 1 in the potential determines the energy spectrum dependence upon the momentum of motion of the two-particle system across the magnetic field like in [10], [11], [21].…”

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

confidence: 99%

“…Relativistic properties of positronium in a strong magnetic field were studied basing on the Bethe-Salpeter equation [9,10]. The nontrivial energy dependence upon the transversal (pseudo)momentum component of the center-of-mass was found in [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…The nontrivial energy dependence upon the transversal (pseudo)momentum component of the center-of-mass was found in [10,11]. Although the Bethe-Salpeter equation is fully relativistic, it was used within the customary "equal-time"…”

Section: Introductionmentioning

confidence: 99%

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

Shabad

Усов

2006

Phys. Rev. D

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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.

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Section: Two-dimensional Bethe-salpeter Equation For Positron-iummentioning

confidence: 99%