Modification of the Coulomb law in a strong magnetic field

Loskutov, Yu. M.; Скобелев, В. В.

doi:10.1016/0375-9601(71)90281-7

Cited by 7 publications

(16 citation statements)

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“…Although much work has been devoted to study of electromagnetic wave propagation in the magnetized vacuum, problems of electro-and magneto-statics in this medium did not attract sufficient attention, save Refs. [5,6], where corrections to the Coulomb law were found when these are small: for B/B 0 ≪ 1 in [5], or at large distances from the source for 1 ≪ B/B 0 ≪ 3παIn this Letter, we find that for sufficiently large b ≡ B/B 0 ≫ 1 the electric field produced by a pointlike charge at rest may be significantly modified by the vacuum polarization, the modification being determined by the characteristic factor αb. The modified Coulomb potential in the close vicinity of its charge, characterized by the Larmour length L B = (eB) −1/2 = (1/m √ b), goes steeper than the standard one, following a Yukawa law, whereas it obeys a long-range "anisotropic Coulomb law" far from the source, at distances characterized by the electron Compton length m…”

mentioning

confidence: 60%

“…At small distances all the dashed curves in Figs. 1 and 2 approach the thick solid Coulomb curve in accord with (5).…”

mentioning

confidence: 77%

“…As b → ∞ the region in Fig.1 between the potential curve and the abscissa below the point −eV ≈ −1.4 × 2αZm, where it is crossed by the envelope, becomes infinitely deep and thin. The area S = (4π/q) x3 LB A 0 (x 3 , 0)dx 3 calculated with expression (5), where x 3 is found from the equation A 0 (x 3 , 0) = V , has a finite limit if and only if C grows proportionally to 1/L B . This is the case: when calculated following Eq.…”

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confidence: 99%

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Modified Coulomb Law in a Strongly Magnetized Vacuum

Shabad

Усов

2007

Phys. Rev. Lett.

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We study electric potential of a charge placed in a strong magnetic field B ≫ B0 = 4.4 · 10 13 G, as modified by the vacuum polarization. In such field the electron Larmour radius is much less than its Compton length. At the Larmour distances a scaling law occurs, with the potential determined by a magnetic-field-independent function. The scaling regime implies short-range interaction, expressed by Yukawa law. The electromagnetic interaction regains its long-range character at distances larger than the Compton length, the potential decreasing across B faster than along. Correction to the nonrelativistic ground-state energy of a hydrogenlike atom is found. In the limit B = ∞, the modified potential becomes the Dirac δ-function plus a regular background. With this potential the ground-state energy is finite -the best pronounced effect of the vacuum polarization.PACS numbers: 03.50, 77.22.Ch, 97.60.Gb There is now compelling evidence that many compact astronomical objects (soft gamma-ray repeaters, anomalous X-ray pulsars, and some radio pulsars) identified with neutron stars have surface magnetic fields as high as ∼ 10 14 − 10 15 G [1]. More strong magnetic fields (B ∼ 10 16 − 10 17 G) are predicted to exist at the surface of cosmological gamma-ray bursters if they are rotationpowered neutron stars similar to radio pulsars [2]. All these fields, however, are much smaller than the maximum value inherent in quantum electrodynamics [3].Vacuum in an external magnetic field B behaves as an anisotropic dielectric medium with spatial and frequency dispersion, (e.g., [4]). These properties may become important, provided that the field strength achieves the characteristic value B 0 = m 2 /e ≃ 4.4×10 13 G, where m is the electron mass and e is its charge. [Henceforth, we set = c = 1 and refer to the Heaviside-Lorentz system of units.] Although much work has been devoted to study of electromagnetic wave propagation in the magnetized vacuum, problems of electro-and magneto-statics in this medium did not attract sufficient attention, save Refs. [5,6], where corrections to the Coulomb law were found when these are small: for B/B 0 ≪ 1 in [5], or at large distances from the source for 1 ≪ B/B 0 ≪ 3παIn this Letter, we find that for sufficiently large b ≡ B/B 0 ≫ 1 the electric field produced by a pointlike charge at rest may be significantly modified by the vacuum polarization, the modification being determined by the characteristic factor αb. The modified Coulomb potential in the close vicinity of its charge, characterized by the Larmour length L B = (eB) −1/2 = (1/m √ b), goes steeper than the standard one, following a Yukawa law, whereas it obeys a long-range "anisotropic Coulomb law" far from the source, at distances characterized by the electron Compton length m(Details of the corresponding derivations can be found in the accompanying preprint [7]). The short-range part of the modified potential tends to the Dirac δ-function in the limit b → ∞. The modification of the Coulomb law should affect, first of all, the field of...

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mentioning

confidence: 60%

“…At small distances all the dashed curves in Figs. 1 and 2 approach the thick solid Coulomb curve in accord with (5).…”

mentioning

confidence: 77%

mentioning

confidence: 99%

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Modified Coulomb Law in a Strongly Magnetized Vacuum

Shabad

Усов

2007

Phys. Rev. Lett.

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“…3 stick closer and closer to the vertical axis, the spacing between the curves and this axis becoming infinitely thin in the limit b = ∞. The area (q/2π)S of the region restricted by any curve (24) and the x 3 -axis in the domain…”

Section: B the Limiting B = ∞ Formmentioning

confidence: 92%

“…[24,25], where corrections to the Coulomb law were found when these are small: for B/B 0 ≪ 1 in [24], or at large distances from the source for 1 ≪ B/B 0 ≪ 3πα −1 in [25], where α = e 2 /4π = 1/137 in the fine-structure constant.…”

Section: Introductionmentioning

confidence: 99%

Electric field of a pointlike charge in a strong magnetic field and ground state of a hydrogenlike atom

Shabad

Усов

2008

Phys. Rev. D

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In an external constant magnetic field, so strong that the electron Larmour length is much shorter than its Compton length, we consider the modification of the Coulomb potential of a point charge owing to the vacuum polarization. We establish a short-range component of the static interaction in the Larmour scale, expressed as a Yukawa-like law, and reveal the corresponding "photon mass"parameter. The electrostatic force regains its long-range character in the Compton scale: the tail of the potential follows an anisotropic Coulomb law, decreasing away from the charge slower along the magnetic field and faster across. In the infinite-magnetic-field limit the potential is confined to an infinitely thin string passing though the charge parallel to the external field. This is the first evidence for dimensional reduction in the photon sector of quantum electrodynamics. The one-dimensional form of the potential on the string is derived that includes a δ-function centered in the charge. The nonrelativistic ground-state energy of a hydrogenlike atom is found with its use and shown not to be infinite in the infinite-field limit, contrary to what was commonly accepted before, when the vacuum polarization had been ignored. These results may be useful for studying properties of matter at the surface of extremely magnetized neutron stars.

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Polarization operator of a photon in an ultraintense magnetic field

Скобелев¹

1975

Soviet Physics Journal

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Modification of the Coulomb law in a strong magnetic field

Cited by 7 publications

References 2 publications

Modified Coulomb Law in a Strongly Magnetized Vacuum

Modified Coulomb Law in a Strongly Magnetized Vacuum

Electric field of a pointlike charge in a strong magnetic field and ground state of a hydrogenlike atom

Polarization operator of a photon in an ultraintense magnetic field

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