Regular electrically charged objects in Nonlinear Electrodynamics coupled to Gravity

We present a brief review of the basic properties of regular electrically charged black holes and electromagnetic solitons, predicted by analysis of regular solutions to dynamical equations of Nonlinear Electrodynamics minimally coupled to Gravity (NED-GR). The fundamental generic feature of regular NED-GR objects is the de Sitter vacuum interiors and the relation of their masses to spacetime symmetry breaking from the de Sitter group. Regular spinning NED-GR objects have interior de Sitter vacuum disk with the properties of a perfect conductor and ideal diamagnetic. The disk is confined by the ring with the superconducting current which provides the non-dissipative source of the electromagnetic fields and of the intrinsic magnetic momentum.

Conjugate spinor field equation for massless spin-3/2 field in de Sitter ambient space

The quantum field theory in de Sitter ambient space provide us with a comprehensive description of massless gravitational field. Using the gauge-covariant derivative in the de Sitter ambient space, the gauge invariant Lagrangian density has been found.In this paper, the equation of the conjugate spinor for massless spin-$\frac{3}{2}$ field is obtained by Euler-Lagrange equation. Then the field equation is written in terms of the Casimir operator of the de Sitter group. Finally, the gauge invariant field equation is presented.

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).

On the Group-Theoretical Approach to Relativistic Wave Equations for Arbitrary Spin

Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer–Duffin equations for particles of arbitrary spin are investigated. It is proved that an irreducible relativistic equation formulated using spin matrices satisfying the commutation relations of the de Sitter group leads to inconsistent results, mainly as a consequence of violation of unitarity and the appearance of a mass spectrum that does not reflect the physical reality of elementary particles. However, the introduction of subsidiary conditions resolves the problem of unitarity and restores the physical meaning of the mass spectrum. The equations obtained by these approaches are solved and the physical nature of the solutions is discussed.

Polarization tensor in de Sitter gauge gravity

The gauge theory of the de Sitter group, [Formula: see text], in the ambient space formalism has been considered in this paper. This method is important to construction of the de Sitter super-conformal gravity and Quantum gravity. [Formula: see text] gauge vector fields are needed which correspond to [Formula: see text] generators of the de Sitter group. Using the gauge-invariant Lagrangian, the field equations of these vector fields have been obtained. The gauge vector field solutions are recalled. By using these solutions, the spin-[Formula: see text] gauge potentials has been constructed. There are two possibilities for presenting this tensor field: rank-[Formula: see text] symmetric and mixed symmetry rank-[Formula: see text] tensor fields. To preserve the conformal transformation, a spin-[Formula: see text] field must be represented by a mixed symmetry rank-[Formula: see text] tensor field, [Formula: see text]. This tensor field has been rewritten in terms of a generalized polarization tensor field and a de Sitter plane wave. This generalized polarization tensor field has been calculated as a combination of vector polarization, [Formula: see text], and tensor polarization of rank-2, [Formula: see text], which can be used in the gravitational wave consideration. There is a certain extent of arbitrariness in the choice of this tensor and we fix it in such a way that, in the limit, [Formula: see text], one obtains the polarization tensor in Minkowski spacetime. It has been shown that under some simple conditions, the spin-[Formula: see text] mixed symmetry rank-[Formula: see text] tensor field can be simultaneously transformed by unitary irreducible representation of de Sitter and conformal groups ([Formula: see text]).

Graphene in curved Snyder space

The Snyder-de Sitter (SdS) model which is invariant under the action of the de Sitter group, is an example of a noncommutative space-time with three fundamental scales. In this paper, we considered the massless Dirac fermions in graphene layer in a curved Snyder space-time which are subjected to an external magnetic field. We employed representation in the momentum space to derive the energy eigenvalues and the eigenfunctions of the system. Then, we used the deduced energy function obtaining the internal energy, heat capacity, and entropy functions. We investigated the role of the fundamental scales on these thermal quantities of the graphene layer. We found that the effect of the SdS model on the thermodynamic properties is significant.

Integration of Dirac’s Efforts to Construct a Quantum Mechanics Which is Lorentz-Covariant

The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he attempted to construct a representation of the Lorentz group using a normalizable Gaussian function localized both in the space and time variables. In 1949, he introduced his instant form to exclude time-like oscillations. He also introduced the light-cone coordinate system for Lorentz boosts. Also in 1949, he stated the Lie algebra of the inhomogeneous Lorentz group can serve as the uncertainty relations in the Lorentz-covariant world. It is possible to integrate these three papers to produce the harmonic oscillator wave function which can be Lorentz-transformed. In addition, Dirac, in 1963, considered two coupled oscillators to derive the Lie algebra for the generators of the O(3,2) de Sitter group, which has ten generators. It is proven possible to contract this group to the inhomogeneous Lorentz group with ten generators, which constitute the fundamental symmetry of quantum mechanics in Einstein’s Lorentz-covariant world.

Einstein’s E=mc2 Derivable from Heisenberg’s Uncertainty Relations

Heisenberg’s uncertainty relation can be written in terms of the step-up and step-down operators in the harmonic oscillator representation. It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the S p ( 2 ) group which is isomorphic to the Lorentz group applicable to one time-like dimension and two space-like dimensions, known as the O ( 2 , 1 ) group. This group has three independent generators. The one-dimensional step-up and step-down operators can be combined into one two-by-two Hermitian matrix which contains three independent operators. If we use a two-variable Heisenberg commutation relation, the two pairs of independent step-up, step-down operators can be combined into a four-by-four block-diagonal Hermitian matrix with six independent parameters. It is then possible to add one off-diagonal two-by-two matrix and its Hermitian conjugate to complete the four-by-four Hermitian matrix. This off-diagonal matrix has four independent generators. There are thus ten independent generators. It is then shown that these ten generators can be linearly combined to the ten generators for Dirac’s two oscillator system leading to the group isomorphic to the de Sitter group O ( 3 , 2 ) , which can then be contracted to the inhomogeneous Lorentz group with four translation generators corresponding to the four-momentum in the Lorentz-covariant world. This Lorentz-covariant four-momentum is known as Einstein’s E = m c 2 .