Constraining Born-Infeld-like Nonlinear Electrodynamics Using Hydrogen's Ionization Energy

In this work, the hydrogen's ionization energy was used to constrain the free parameter $b$ of three Born-Infeld-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 $b>5.37\times10^{20}K\frac{V}{m}$, where $K=2$, $4\sqrt{2}/3$ and $\sqrt{\pi}$ 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.Comment: 9 pages, 1 figure, references adde

The relation between classical and quantum electrodynamics

In this article it is presented the idea that quantum electrodynamics presents intrinsic limitations in the description of physical processes that makes it impossible to recover from it the type of description we have with classical electrodynamics. In this way I cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as an independent theory but just as an upgrade of classical electrodynamics and the theory of relativity, which permits an extension of classical theory in the description of phenomena that, while being clearly related to the conceptual framework of the classical theory – the description of matter, radiation, and their interaction –, cannot be properly addressed from the classical theory

Remarks on nonlinear Electrodynamics

We consider both generalized Born-Infeld and Exponential Electrodynamics. The field-energy of a point-like charge is finite only for Born-Infeld-like Electrodynamics. However, both Born-Infeld-type and Exponential Electrodynamics display the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy for both classes of Electrodynamics, within the framework of the gauge-invariant path-dependent variables formalism. These are shown to result in long-range ($1/r^5$- type) corrections to the Coulomb potential. Once again, for their non-commutative versions, the interaction energy is ultraviolet finite.Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1312.515

Formulation of Electrodynamics with an External Source in the Presence of a Minimal Measurable Length

In a series of papers, Quesne and Tkachuk (J. Phys. A: Math. Gen. \textbf{39}, 10909 (2006); Czech. J. Phys. \textbf{56}, 1269 (2006)) presented a $D+1$-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal measurable length. In this paper, the Lagrangian formulation of electrodynamics in a 3+1-dimensional space-time described by Quesne-Tkachuk algebra is studied in the special case $\beta'=2\beta$ up to first order over the deformation parameter $\beta$. It is demonstrated that at the classical level there is a similarity between electrodynamics in the presence of a minimal measurable length (generalized electrodynamics) and Lee-Wick electrodynamics. We obtain the free space solutions of the inhomogeneous Maxwell's equations in the presence of a minimal length. These solutions describe two vector particles (a massless vector particle and a massive vector particle). We estimate two different upper bounds on the isotropic minimal length. The first upper bound is near to the electroweak length scale $(\ell_{electroweak}\sim 10^{-18}\, m)$, while the second one is near to the length scale for the strong interactions $(\ell_{strong}\sim 10^{-15}\, m)$. The relationship between the Gaete-Spallucci nonlocal electrodynamics (J. Phys. A: Math. Theor. \textbf{45}, 065401 (2012)) and electrodynamics with a minimal length is investigated.Comment: 13 pages, no figur