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It has been argued that in noncommutative field theories, sizes of physical objects cannot be taken smaller than an "elementary length" related to noncommutativity parameters. By gaugecovariantly extending field equations of noncommutative U (1) ⋆ -theory to cover the presence of external sources, we find electric and magnetic fields produced by an extended static charge. We find that such a charge, apart from being an ordinary electric monopole, is also a magnetic dipole.By writing off the existing experimental clearance in the value of the lepton magnetic moments for the present effect, we get the bound on noncommutativity at the level of 10 4 TeV.

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“…In such a case, one can find [7] many interesting similarities and differences with the QED effects [20].…”

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Noncommutative magnetic moment of charged particles

et al. 2011

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“…At magnetic field strengths far in excess of B cr , the effects of photon dispersion and wave function renormalisation become important for parallel-polarized photons (eg: Hattori and Itakura (2013); Shabad and Usov (2010) and references therein). This is clearly evident in the work by Chistyakov and Rumyantsev (2009) who investigated the Compton effect in a strongly magnetized (B = 200B cr ) medium consisting of both vacuum and plasma contributions.…”

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Resonant Compton scattering associated with pair creation

Weise

2014

Astrophys Space Sci

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Studies of Compton scattering by relativistic electrons in a strong magnetic field have been restricted to either incident photon angles θ ′ aligned along the magnetic field B or incident photon energies ω ′ below the first pair creation threshold ω ′ P C . When these restrictions are relaxed there is a resonance in Compton scattering associated with pair creation (PC), that is analogous to but independent of known resonances associated with gyromagnetic absorption (GA). As with the GA resonances, that may be labeled by the Landau quantum numbers of the relevant states, there is a sequence of PC resonances where the scattering cross section diverges. In this paper, the lowest divergence is studied for incident photon energies satisfying ω ′ 2 sin 2 θ ′ /(2eB) ≪ 1, assuming that the scattering electron is in its ground (Landau) state. This lowest resonance affects only parallel-polarized photons.

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“…In an asymptotically strong magnetic field this equation may be written in the following (1+1)-dimensional form (see our detailed paper [14] for the derivation), covariant under the Lorentz transformations along the axis 3:…”

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“…Equations for the rest two invariant coefficients, other than the singlet Φ, are considered in [14].…”

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Positronium Collapse and the Maximum Magnetic Field in Pure QED

Shabad

Усов

2006

Phys. Rev. Lett.

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A maximum 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 disappearance of the energy gap separating the electron-positron system from the vacuum. The compensation becomes possible owing to the falling to the center phenomenon. The maximum magnetic field may be related to the vacuum and describe its structure.PACS numbers: 03.65. Ge, 03.65.Pm, 12.20.Ds, 98.80.Cq A common feature of compact astronomical objects: white dwarfs, neutron stars, and accretion disks around black holes, is a very strong magnetic field. It is believed that neutron stars possess the strongest observed magnetic fields. The field strength is in the range from ∼ 10 8 G to ∼ 10 14 G for radio pulsars identified with rotation-powered neutron stars [1], and may be as high as ∼ 10 15 G for soft gamma-ray repeaters [2], or even higher (∼ 10 16 − 10 17 G) for the sources of cosmological gamma-ray bursts [3]. Much more intense magnetic fields have been conjectured to be involved in several astrophysical phenomena. For instance, superconductive cosmic strings, if they exist, may have magnetic fields up to ∼ 10 47 − 10 48 G in their vicinities [4]. Magnetic fields of ∼ 10 47 G may be also produced in our Universe at the beginning of the inflation [5]. The fundamental physical problems are how large the field strength can be in nature, and how the properties of the vacuum change when magnetic fields approach the extremity. It is accepted that magnetic fields are stable in pure quantum electrodynamics (QED), and another interaction (weak or strong) or magnetic monopoles have to be involved to make the magnetized vacuum unstable [6].In this Letter, working solely in QED, we find that there exists a maximum value of the magnetic field that delimits the range of its values admitted without revising QED. Its value is many orders of magnitude less than B = B 0 exp(3π/α) (here α = e 2 /4π ≃ 1/137, B 0 = m 2 /e = 4.4 × 10 13 Gauss, m is the electron mass, = c = 1 throughout), the value that restricts the range of validity of QED due to the lack of asymptotic freedom [7]. The maximum magnetic field causes the shrinking of the energy gap between an electron and positron.We exploit the unboundedness from below of the energy spectrum for sufficiently singular attractive potentials, known as the "falling to the center" [8]. For e + e − system in a magnetic field B this phenomenon is caused by the ultraviolet singularity of the photon propagator and occurs in the limit B → ∞. It takes place independently of whether nonrelativistic or relativistic description is used, and is associated with dimensional reduction due to the charged particles being restricted to the lowest Landau levels (see the pioneering work of Loudon [9] and other works out of which most important for our present theme are [9] -[11]). Using the Bethe-Salpeter (BS) equation for the electron-positron system, with the relative motion of the two particles treated in a strictly relat...

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Shabad and Usov Reply:

Cited by 74 publications

References 5 publications

Noncommutative magnetic moment of charged particles

Noncommutative magnetic moment of charged particles

Resonant Compton scattering associated with pair creation

Positronium Collapse and the Maximum Magnetic Field in Pure QED

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