Image of the Electron Suggested by Nonlinear Electrodynamics Coupled to Gravity

We present a systematic review of the basic features that were adopted for different electron models and show, in a brief overview, that, for electromagnetic spinning solitons in nonlinear electrodynamics minimally coupled to gravity (NED-GR), all of these features follow directly from NED-GR dynamical equations as model-independent generic features. Regular spherically symmetric solutions of NED-GR equations that describe electrically charged objects have obligatory de Sitter center due to the algebraic structure of stress–energy tensors for electromagnetic fields. By the Gürses-Gürsey formalism, which includes the Newman–Janis algorithm, they are transformed to axially symmetric solutions that describe regular spinning objects asymptotically Kerr–Newman for a distant observer, with the gyromagnetic ratio g=2. Their masses are determined by the electromagnetic density, related to the interior de Sitter vacuum and to the breaking of spacetime symmetry from the de Sitter group. De Sitter center transforms to the de Sitter vacuum disk, which has properties of a perfect conductor and ideal diamagnetic. The ring singularity of the Kerr–Newman geometry is replaced with the superconducting current, which serves as the non-dissipative source for exterior fields and source of the intrinsic magnetic momentum for any electrically charged spinning NED-GR object. Electromagnetic spinning soliton with the electron parameters can shed some light on appearance of a minimal length scale in the annihilation reaction e+e−→γγ(γ).

Mass, Spacetime Symmetry, de Sitter Vacuum, and the Higgs Mechanism

We address the question of the intrinsic relation between mass, gravity, spacetime symmetry, and the Higgs mechanism implied by involvement of the de Sitter vacuum as its basic ingredient (a false vacuum). Incorporating the de Sitter vacuum, the Higgs mechanism implicitly incorporates the generic relation between mass, gravity, and spacetime symmetry revealed in the frame of General Relativity for all objects involving the de Sitter vacuum. We overview two observational cases which display and verify this relation, the case known as “negative mass square problem” for neutrino, and appearance of a minimal length scale in e + e − annihilation.

q-Deformed superstatistic thermodynamics in the presence of minimal length quantum mechanics

In this paper, we study the thermodynamic properties of a quantum oscillator in the presence of the minimal length scale in terms of the q-deformed superstatistics of statistical mechanics. We evaluated the partition function from the Boltzmann factor and obtained other thermodynamic properties such as internal energy, Helmholtz free energy, entropy, and specific heat capacity. We have also shown graphically the effects of the minimal length and the q-statistical properties on the thermodynamic properties of the system.

Application of Biot–Savart law and generalized uncertainty principle

In the recent decade, many investigations have been done in the framework of generalized uncertainty principle (GUP), but the phenomenology of models in this framework are less studied. In this work, the applications of Biot–Savart law in the presence of a minimal length scale are investigated. We obtain the modified magnetostatic field from an infinitely long, straight wire carrying current [Formula: see text]. Also, the modified magnetostatic field from a circular loop carrying current [Formula: see text] and the modified magnetostatic field of an ideal solenoid are found. It is interesting to note that in the limit [Formula: see text], all of the modified magnetostatic fields become their usual forms.

Covariant GUP Deformed Hamilton-Jacobi Method

We first briefly revisit the original Hamilton-Jacobi method and show that the Hamilton-Jacobi equation for the action I of tunneling of a fermionic particle from a charged black hole can be written in the same form of that for a scalar particle. On the other hand, various theories of quantum gravity suggest the existence of a minimal length scale, incorporating of which into quantum mechanics implies a modification of the uncertainty principle. In the scenario incorporating the generalized uncertainty principle (GUP) into a quantum field theory (QFT) in a covariant way, we derive the deformed model-independent KG/Dirac and Hamilton-Jacobi equations using the methods of effective field theory. For this Lorentz invariant GUP modified QFT, we find that the effect of GUP on the Hamilton-Jacobi equations is simply to “renormalize” the mass of the emitted particles, from m to meff. Therefore, in this scenario, the Hawking temperature of a black hole does not receive any corrections from the GUP effect.

Quantum electrodynamics and the electron self-energy in a deformed space with a minimal length scale

The main motivation to study models in the presence of a minimal length is to obtain a quantum field theory free of the divergences. In this way, in this paper, we have constructed a new framework for quantum electrodynamics embedded in a minimal length scale background. New operators are introduced and the Green function method was used for the solution of the field equations, i.e. the Maxwell, Klein–Gordon and Dirac equations. We have analyzed specifically the scalar field and its one loop propagator. The mass of the scalar field regularized by the minimal length was obtained. The QED Lagrangian containing a minimal length was also constructed and the divergences were analyzed. The electron and photon propagators, and the electron self-energy at one loop as a function of the minimal length was also obtained.