Abstract
Selection rules that follow from parity and four-momentum conservation are listed for head-on light-by-light scattering in a strong magnetic field taking into account nontrivial dispersion laws of different photon eigen-modes. The wave-length shifts occur for certain transitions between photon eigen-modes.
Highlights
Contrary to the classical electrodynamics of Faraday–Maxwell, the quantum theory of electromagnetic fields, i.e., the theory of the interaction of electrons, positrons, and other charged particles with photons (QED), is nonlinear in the sense that electromagnetic fields are not mutually independent, but they interact between/with themselves
The nonlinearity of QED has a great number of possible manifestations, an important one among them being the interaction of a photon with a strong external field, its effect being equivalent [1,2,3] to a sort of anisotropic, linear or nonlinear, homogeneous or inhomogeneous, medium
It is interesting to note that, when the nonlinearity is determined by the Heisenberg–Euler Lagrangian, a traveling-wave solution of nonlinear Maxwell equations is provided by a dispersion law that involves a dependence on the amplitudes of the traveling wave [19]
Summary
Contrary to the classical electrodynamics of Faraday–Maxwell, the quantum theory of electromagnetic fields, i.e., the theory of the interaction of electrons, positrons, and other charged particles with photons (QED), is nonlinear in the sense that electromagnetic fields are not mutually independent, but they interact between/with themselves. The ultrarelativistic charged colliding bodies exchange with two (large intensity beams of) GeV-photons that scatter one another This process was observed [15] with the LHC in the course of the ATLAS experiment and is viewed as the first experimental evidence of the light-by-light scattering. While the possibility that this magnetic field may open the reaction of two-photon merging under the existing conditions of the ultraperipheral collision is left aside for the time being, the light-by-light scattering is attracting attention. It is interesting to note that, when the nonlinearity is determined by the Heisenberg–Euler Lagrangian, a traveling-wave solution of nonlinear Maxwell equations is provided by a dispersion law that involves a dependence on the amplitudes of the traveling wave [19] This is, certainly, not our case, since we deal with the propagation of small-amplitude waves governed by equations linearized near an external field. Essential as well is the change of the photon wave-length depending (for parallel incidence) or not depending (for perpendicular incidence) on the scattering angle
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