In this work, the hydrogen's ionization energy was used to constrain the free parameter b of three BornInfeld-like electrodynamics namely Born-Infeld itself, Logarithmic electrodynamics and Exponential electrodynamics. An analytical methodology capable of calculating the hydrogen ground state energy level correction for a generic nonlinear electrodynamics was developed. Using the experimental uncertainty in the ground state energy of the hydrogen atom, the bound b > 5.37 × 10 20 K V m , where K = 2, 4 √ 2/3 and √ π for the Born-Infeld, Logarithmic and Exponential electrodynamics respectively, was established. In the particular case of Born-Infeld electrodynamics, the constraint found for b was compared with other constraints present in the literature.

The recent light-by-light scattering cross section measurement made by the ATLAS Collaboration is used to constrain nonlinear corrections to Maxwell electrodynamics parametrized by the Lagrangian L = F + 4αF 2 + 4βG 2 + 4δFG. The ion's radiation is described using the equivalent photon approximation, and the influence of four different nuclear charge distributions is evaluated. Special attention is given to the interference term between the Standard Model and the nonlinear corrections amplitudes. By virtue of the quadratic dependence on α, β and δ, the nonlinear contribution to the Standard Model γγ cross section is able to delimit a finite region of the parameter's phase space. The upper values for α, β in this region are of order 10 −10 GeV −4 , a constraint of at least 12 orders of magnitude more precise when compared to low-energy experiments. An upper value of the same order for δ is obtained for the first time in the LHC energy regime. We also give our predictions for the Standard Model cross section measured at ATLAS for each distribution and analyze the impact of the absorption factor. We finally give predictions for the future measurements to be done with upgraded tracking acceptance |η| < 4 by the ATLAS Collaboration.

In this paper we analyze the thermodynamic properties of a photon gas under the influence of a background electromagnetic field in the context of any nonlinear electrodynamics. Neglecting the selfinteraction of photons, we obtain a general expression for the grand canonical potential. Particularizing for the case when the background field is uniform, we determine the pressure and the energy density for the photon gas. Although the pressure and the energy density change when compared with the standard case, the relationship between them remains unaltered, namely ρ = 3p. Finally, we apply the developed formulation to the cases of Heisenberg-Euler and Born-Infeld nonlinear electrodynamics. For the Heisenberg-Euler case, we show that our formalism recovers the results obtained with the 2-loop thermal effective action approach.

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