Vínculos de eletrodinâmicas não lineares

Abstract

Nonlinear electrodynamics (NLED) are a generalization of Maxwell’s electrodynamics that arises and is used in several fields such as: gravitation, classical consequences of the quantum vacuum, low energy limits of string theories etc. Because of this, it is an important task to evaluate the empirical validity of these theories by comparing their predictions with the corresponding experimental measurements. In this thesis, the ionization energy of the hydrogen atom and the photon-photon scattering cross section recently observed by the ATLAS Collaboration with ultraperipheral collisions of lead ions are used. The way in which Born-Infeld-like theories, a class of NLED, modify the Coulomb potential produced by the hydrogen atom’s nucleus is calculated. Then, using the perturbation theory, the first order correction of the ground state energy is derived. It is remarkable that, although this class of NLED behaves identically in the low energy limit, each theory produces a slightly different correction. This is due to the framework of perturbation theory which forces the use of the complete Lagrangian. Comparison with the measurement of the ionization energy constrains the parameter b, which characterizes this class of theories, to be b & 1021V m−1 . The direct interaction between photons is one of the most striking features of NLED. Therefore, the cross section for γγ → γγ scattering acquires a contribution due to nonlinear corrections to Maxwell’s Lagrangian besides the Standard Model ones. In the equivalent photon approximation, the complete scattering cross section for Pb Pb → Pb Pb + γγ in ultraperipheral collisions is derived through the convolution of the subprocess cross section γγ → γγ with the photon fluxes produced by the ions. Comparison of the complete cross section with the experimental measurement obtained by the ATLAS Collaboration yields the most precise constrain for the nonlinear parameters α ∼ β . 2 × 10−10GeV−4 ≈ 10−47m3 J −1.