Nonlinear electrodynamics coupled to teleparallel theory of gravity

Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy--momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy--momentum we obtain the value of energy.     

Nonlinear electrodynamics and anisotropic space-time

The metrical properties of four-space in the presence of a nonlinear electromagnetic field in vacuum are investigated. It is shown that the metric induced by the nonlinear electromagnetic field has a complicated nature and corresponds to an anisotropic space-time, i.e., to a four-space in which birefringence is observed. A special case of such a space is ordinary Riemann-Euclid space. As an example, the influence on the metric of the radiative corrections that follow from quantum electrodynamics is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 52–55, April, 1980.     

Nonlinear arcsin‐electrodynamics

A new model of nonlinear electrodynamics with three parameters is suggested and investigated. It is shown that if the external constant magnetic field is present the phenomenon of vacuum birefringence takes place. The indices of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field are calculated. The electric field of a point‐like charge is not singular at the origin and the static electric energy is finite. We have calculated the static electric energy of point‐like particles for different parameters of the model. The canonical and symmetrical Belinfante energy‐momentum tensors and dilatation current are obtained. We demonstrate that the dilatation symmetry and dual symmetry are broken in the model suggested.

     

Coulomb law and hypercomplex approach to electrodynamics

For a Coulomb-type field of a single point charge, generalized expressions are considered which are obtained on the basis of a hypercomplex generalization of electrodynamics with magnetic charges [1]. Along with the usual electrostatic field, in this approach a single charge can create a magnetic field, provided that the space points around the charge are oriented in a different way than the field source (charge) itself. Aside from vector fields, such a charge can create scalar and pseudoscalar fields, if time flows differently at the field points around the charge than at the location of the charge, or if the charge itself moves with respect to a fixed reference frame. The sources of the dual symmetry of the Maxwell equations are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 101–104, September, 1990.     

Nonlinear electrodynamics in space-times with torsion

A nonminimal and nongauge invariant descirption of nonlinear electrodynamics in space-times with torsion is given. It is shown that in the case of the Weitzenböck teleparallel space-time, massive photons are produced by a mechanism which involves the nonminimal coupling constant and the divergence of the torsion vector.On leave of absence from: Grupo de Relatividade e Teoria de Campo, Instituto de Fisica — UERJ, Departamento de Fisica Teorica, 20550 Maracan, Rio de Janeiro, Brazil     

Nonlinear electrodynamics near a superconducting string

We calculate the effective action for photons in an arbitrary external field using the expansion in the inverse of the mass of the electron. The resulting effective lagrangian is used to calculate magnetization of the vacuum in the vicinity of a superconducting string. The magnetization current partially screens the current in the string and slows down the rate of growth of the current there. We also discuss the scattering of electromagnetic waves on a superconducting string with the nonlinear effects taken into account.     

An approach to introducing fractional integro-differentiation in classical electrodynamics

Analogs for Maxwell’s equations with fractional derivatives are obtained using the concepts of an effective current and the velocity of a charged particle in a medium. The calibration invariance is considered and a diffusion-wave equation is found and analyzed for scalar and vector potentials. It is shown that the stochastic nature of charged particle motion in a medium influences the dynamics of an electromagnetic field.     

Non-perturbative approach to the electrodynamics of rough metal surfaces

Surface plasmon (SP) effects on the optical properties of rough metal surfaces are considered. Angular and frequency dependences of radiation, arising from SP decay and diffuse light scattering, as well as the photoemission current from a rough metal surface have been calculated. The above effects have been shown to be strongly enhanced when SP attenuation lengths stipulated by SP decay into vacuum and absorption in the metal, are much larger than the attenuation length stipulated by transformations into other SP states. Possibilities of comparing theoretical calculations with experimental data are considered.     

Nonlinear electrodynamics in a superstrong magnetic field

Using a Feynman technique in a two-dimensional space we have calculated an electron propagator and a photon polarization tensor in a superstrong magnetic field $\text{B ? B}{}_{\mathrm{<mtext>0</mtext>}}\text{=}\text{m}{}^{\mathrm{<mtext>2</mtext>}}\text{e}\text{=}\text{4.41 × 10}{}^{13}$ G. Some applications are briefly discussed.     

Quantum-trajectory approach to cavity quantum electrodynamics with up to three-atom collective effects

We present a quantum-trajectory treatment of the dynamics of a high-Q cavity mode interacting with a low-density atomic beam in the strong coupling regime. We consider up to three-atom collective effects, and evaluate their contribution to the destabilization of cavity field trapping states for mean number of atoms in the cavity both much smaller than one (micromaser or microlaser), and on the order of one (approaching a mesoscopic regime).     

New approach to nonlinear electrodynamics: Dualities as symmetries of interaction

The duality-symmetric nonlinear electrodynamics in a new formulation with auxiliary tensor fields is considered. The Maxwell field strength appears only in bilinear terms of the corresponding generic Lagrangian, while the self-interaction is represented by a function E depending on the auxiliary fields. Two types of dualities inherent in the nonlinear electrodynamics admit a simple off-shell characterization as symmetry properties of this function. In the standard formulation, the continuous U(1) duality symmetry is nonlinearly realized on the Maxwell field strength. In the new setting, the same symmetry acts as linear U(1) transformations of the auxiliary field variables. The nonlinear U(1) duality condition proves to be equivalent to the U(1) invariance of the self-interaction E. The discrete self-duality (or self-duality by Legendre transformation) amounts to a weaker reflection symmetry of E. For a class of duality-symmetric Lagrangians, an alternative representation with the auxiliary scalar field is introduced and new explicit examples of such systems are found.     

Nonlinear electrodynamics and particle-like solutions with consideration of gravitation

The question of existence of various forms of spherically symmetric particle-like solutions within the theory of general relativity with nonlinear electromagnetic fields is considered. Such solutions are those with a regular center and those with a throat and second spatial asymptote. It will be shown that in the given class of theories: 1) particle-like solutions with nonzero magnetic charge do not exist, and 2) particle-like solutions do not exist for gauge invariant Lagrangians. For the class of Lagrangians with explicit dependence upon potential, particle-like solutions of both types are obtained and limits of their parameters are determinedTranslated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 36–40, September, 1989.     

Superfield approach to symmetry invariance in quantum electrodynamics with complex scalar fields

We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the superfields defined on a (4,2)-dimensional supermanifold, is a clear-cut proof for the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST invariance of the corresponding four (3+1)-dimensional (4D) Lagrangian density that describes the interaction between the U(1) gauge field and the charged complex scalar fields. The above 4D field theoretical model is considered on a (4,2)-dimensional supermanifold parametrized by the ordinary four space-time variables x ^μ (with μ = 0, 1, 2, 3) and a pair of Grassmannian variables θ and (with θ ² = ² = 0, θ + θ = 0). Geometrically, the (anti-)BRST invariance is encoded in the translation of the super-Lagrangian density along the Grassmannian directions of the above supermanifold such that the outcome of this shift operation is zero.      

Composite electrodynamics

This paper solidifies the foundations for a singleton theory of light, first proposed two years ago. This theory is based on a pure gauge coupling of the scalar singleton field to the electromagnetic current. Like quarks, singletons are essentially unobservable. The field operators are not local observables and therefore need not commute for spacelike separation. This opens up possibilities for generalized statistics, just as is the case for quarks. It then turns out that a pure gauge coupling, in which ∂μφ(x) couples to the conserved current j^μ(x), generates real interactions— the effective theory is precisely ordinary electrodynamics in de Sitter space. Here we improve our theory and explain it in much more detail than before, adding two new results. (1) The concept of normal ordering in a theory with unconventional statistics is worked out in detail. (2) We have discovered the natural way of including both photon helicities. Quantization, it may be noted, is a study in representation theory of certain infinite-dimensional, nilpotent Lie algebras, of which the Heisenberg algebra is the prototype.