Abstract
Nonlinear corrections on electromagnetic fields in vacuum have been expected. In this study, we have theoretically considered nonlinear Maxwell’s equations in a one-dimensional cavity for a classical light and external static electromagnetic fields. A general solution for the electromagnetic corrective components including that of a longitudinal standing wave was derived after a linearization. The main purpose is to give a detailed feature of the previously reported resonant behavior [Shibata, Euro. Phys. J. D 74:215 (2020)], such as the effect of external static fields and the polarization fluctuation. These results favor the development of new and effective method for experiment.Graphic abstract
Highlights
The classical electromagnetic fields in vacuum are described by the linear Maxwell’s equations
Several theories assert that a nonlinear correction arises from virtual electron–positron pairs, but these have yet to be observed in experiments
The nonlinear correction is considered to affect such as the radiation from pulsars [1,2] or neutron stars [3], the Wichmann–Kroll correction [4] on the Lamb shift, and the interaction between a nucleus and electrons through the Uehling potential [5,6,7]
Summary
The classical electromagnetic fields in vacuum are described by the linear Maxwell’s equations. A cavity system is often used, such as the PVLAS (Polarizzazione del Vuoto con LASer) [15,16], BMV (Birefringence Magnetique du Vide) [17], and OVAL (Observing VAcuum with Laser) experiments [18]. These instruments explore the changes in the refractive index, or birefringence, when light passes through an external magnetic field. We solve the initial and boundary problem and derive the minimum nonlinear correction for a general classical electromagnetic field. We show that the present study does not contradict the calculation of the well-known birefringence
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