Properties of finite amplitude electromagnetic waves propagating in the quantum vacuum

Abstract

We study two counter-propagating electromagnetic waves in the vacuum within the framework of the Heisenberg-Euler formalism in quantum electrodynamics. We show that the non-linear field equations decouple for ordinary wave case and can be solved exactly. We solve the non-linear field equations assuming the solution in a form of a Riemann wave. We discuss the properties of the nonlinear electromagnetic wave propagating in the quantum vacuum, such as the wave steepening, subsequent generation of high order harmonics and electromagnetic shock wave formation with electron-positron pair generation at the shock wave front.The increasing availability of high power lasers raises interest in experimental observation and motivates theoretical studies of non-linear QED in the laser-laser scattering [1][2][3][4][5][6][7][8][9][10][11], scattering of the XFEL emitted photons [12], and the interaction of relatively long wavelength radiation with the X-ray photons [13][14][15], nonlinear laserplasma interaction [16,17] and to complex problems on the boundary of non-linear QED, super intense lasers and plasma, nuclear and particle physics such as theoretical studying of MeV X-rays in a plasma that is generated by femtosecond laser pulses, the study of γ−induced nuclear reactions in plasma radiated by super-intense laser, or neutron production in laser plasma [18][19][20], non-linear cooperative electron-gamma-nuclear, multiphoton and other processes [21-23], fotonuclear physics, nuclear fission and fusion with laser-heated clusters and plasmas [24][25][26][27][28].The results expected to be obtained will allow us to test extensions of the Standard Model, in which new particles can participate in the loop diagrams and provide a window into a new physics (see search for the process in X-ray region [12]).Such non-linear process of light-by-light scattering breaks the linearity of the Maxwell equations and is one of the oldest predictions of quantum electrodynamics QED. The photon-photon scattering in a vacuum occurs via the generation of virtual electron-positron pairs creation resulting in vacuum polarization [29]. To investigate such process it is convenient to use Heisenberg-Euler approach in QED [29][30][31]. This problem was addressed as birefringence effect when the speed of wave propagation depends on the wave polarization, [32,33]. Birefringence was motivated by analogy with the effect in crystalography and means that the incoming light splits into two waves in the vacuum which serves as a medium: the ordinary wave and the extraordinary wave. The ordinary * Hedvika. Kadlecova@eli-beams.eu wave propagates parallel to the optic axis with polarization perpendicular to the optic axis and refractive index n or . Extraordinary wave has polarization in the direction of the optic axis and has refractive index n ex . For example, when unpolarized light enters an uniaxial birefringent material, it is split into two beams travelling different directions. The ordinary ray doesn't change direction while the extraordinary ray is refra...

Electromagnetic shock waves propagating in quantum vacuum

“…(70) later on. We observe that the calculation is quite similar to the one performed in the Heisenberg-Euler approximation of QED theory in [31]. We have obtained the set of two differential equations (20,21).…”

“…We are going to investigate the ordinary wave case in the birefringence problem, therefore we assume E = (0, 0, E z ) and B = (0, B y , 0), which is the simple case of non-vanishing components E z and B y , in order to investigate the crossed field case E • B = 0 which is the setup we have made in our previous work. Surprisingly, for such a case, the Born-Infeld Lagrangian (2) reduces to the Born Lagrangian (1), therefore the following investigation will be done in the Born theory where the shock waves are being generated thanks to presence of the birefringence effect and moreover we can use the method developed in [28,31] to study them.…”

“…As in [28,31], we approach solving the non-linear equations using Riemann wave (simple wave) well known in nonlinear wave theory [29,30,44]. The procedure is almost similar to that one developed in [31], it is thanks to the similar structure of field equations and the universality of the method. The different form of the Born Lagrangian (1) comes in in the form of the coefficients α az , α by , β az , β by and γ az , γ by , (40).…”

“…In our previous papers [28,31], we were proposing experiment to directly detect the photon-photon scattering by detecting the gamma-rays coming from the electronpositron pair formation. In this experiment, we might be able to study also the Born-Infeld (BSM) contribution to the process.…”

Vacuum Birefringence at the Gamma Factory

“…See refs. [37–56] for proposals aiming at probing the effect with optical, X‐ray, synchrotron, or gamma radiation and high‐intensity lasers as pump. For proposals to measure vacuum birefringence induced by a magnetic field with high‐energy photons, cf.…”