Abstract
Vacuum magnetic birefringence is one of the most interesting non-linear phenomena in quantum electrodynamics because it is a pure photon-photon result of the theory and it directly signalizes the violation of the classical superposition principle of electromagnetic fields in the full quantum theory. We perform analytical and numerical calculations when an electromagnetic wave interacts with an oscillating external magnetic field. We find that in an ideal cavity, when the external field frequency is around the electromagnetic wave frequency, the normal and parallel components of the wave suffer parametric resonance at different rates, producing a vacuum birefringence effect growing in time. We also study the case where there is no cavity and the oscillating magnetic field is spatially localized in a region of length $L$. In both cases we find also a rotation of the elliptical axis.
Highlights
Nonlinear effects in the vacuum of quantum electrodynamics (QED) were studied soon after the formulation of QED theory [1], thereby confirming the seminal results obtained even earlier [2,3]
We find that in an ideal cavity, when the external field frequency is around the electromagnetic wave frequency, the normal and parallel components of the wave suffer parametric resonance at different rates, producing a vacuum birefringence effect growing in time
As was pointed out by Schwinger [1], nonlinear effects in QED predominate for fields above the critical values for the electric E 1⁄4 jEj and magnetic B 1⁄4 jBj fields given by Ecr 1⁄4 m2ec3=qeħ ≃ 1.3 × 1018 V=m and Bcr ≃ Ecr=c, where me, qe, ħ stand for the electron mass, the electron charge, and the reduced Planck constant
Summary
Nonlinear effects in the vacuum of quantum electrodynamics (QED) were studied soon after the formulation of QED theory [1], thereby confirming the seminal results obtained even earlier [2,3]. At leading order in a weak field expansion, these nonlinear effects arise from microscopic photon-photon scattering processes mediated by an electron-positron loop featuring four couplings to the photon field [4,5,6,7,8], impacting light propagation in external electromagnetic fields [4,5,6,7], and remaining one of the predictions of QED that has not yet been experimentally corroborated The verification of this QED induced effective photon-photon interaction is the major goal of the PVLAS [9,10,11], BMV [12,13], and OVAL [14] experiments.
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