Regularization of electromagnetic field for self-force problem in de Sitter spacetime

The two-particle system with the time-asymmetric retarded-advanced electromagnetic interaction known as the Staruszkiewicz–Rudd–Hill model is considered in the de Sitter space-time. The manifestly covariant descriptions of the model within the Lagrangian and Hamiltonian formalisms with constraints are proposed. It is shown that the model is de Sitter-invariant and integrable. An explicit solution of the equations of motion is derived. We use the covariant electromagnetic Green function in the de Sitter space in order to derive the equation of motion of a point charge in an external electromagnetic field, where the radiation reaction is taken into account.

In this paper, the two-point function of linearized gravitons on de Sitter (dS) space is presented. Technically, respecting the dS ambient space notation, the field equation is given by the coordinate-independent Casimir operators of the de Sitter group. Analogous to the quantization of the electromagnetic field in Minkowski space, the field equation admits gauge solutions. The notation allows us to exhibit the formalism of Gupta-Bleuler triplets for the present field in exactly the same manner as it occurs for the electromagnetic field. In this regard, centering on the spin-two part (the traceless part, ${\cal{K}}^t$), the field solution is written as a product of a generalized polarization tensor and a minimally coupled massless scalar field. Then, admitting a de Sitter-invariant vacuum through the so-called "Krein space quantization", the de Sitter fully covariant two-point function is calculated. This function is interestingly free of pathological large distance behavior (infrared divergence). Moreover, the spin-zero part (the pure-trace part; ${\cal{K}}^{pt}$) of the field is discussed in this paper. It is shown that the implications of the dS group unitary irreducible representations restrict the gauge-fixing parameter to the optimal value, which remarkably results in the pure-trace part be written in terms of a conformally coupled massless scalar field.

We introduce a methodology for quantitatively measuring at all times in its evolution how close our physical spatially flat [Formula: see text] CDM universe with cosmological constant [Formula: see text] is to the de Sitter spacetime [Formula: see text] with de Sitter radius [Formula: see text]. The main idea in this study is to align the respective scale factors [Formula: see text] and [Formula: see text] of these two spacetimes, where de Sitter spacetime is taken with respect to a spatially flat foliation. This goal is accomplished by fine-tuning an adjustable parameter [Formula: see text] that arises naturally in the de Sitter scale factor by requiring that these scale factors be future-asymptotically convergent. Once this parameter is adjusted and the scale factors are aligned, we define a relative error function [Formula: see text] that computes as a function of time [Formula: see text] how close the scale factors of these two spacetimes are to one another. Our results quantify how close our physical [Formula: see text]CDM universe is to its corresponding de Sitter spacetime as both spacetimes converge as they expand. As an example of our results, we show that at the present time [Formula: see text][Formula: see text]Gy, to an accuracy of [Formula: see text], and at [Formula: see text][Formula: see text]Gy, to an accuracy of [Formula: see text], we can use de Sitter spacetime to model our own [Formula: see text]CDM universe. Our results also show by statistical analysis that with a confidence level of 68.3%, for [Formula: see text][Formula: see text]Gy, the scale factor [Formula: see text] of our [Formula: see text] universe and the scale factor [Formula: see text] of the corresponding de Sitter spacetime are indistinguishable to within the accuracy of current cosmological measurements.

We study and look for similarities between the response rates ${R}^{\mathrm{dS}}{(a}_{0},\ensuremath{\Lambda})$ and ${R}^{\mathrm{SdS}}{(a}_{0},\ensuremath{\Lambda},M)$ of a static scalar source with constant proper acceleration ${a}_{0}$ interacting with a massless, conformally coupled Klein-Gordon field (i) in de Sitter spacetime, in the Euclidean vacuum, which describes a thermal flux of radiation emanating from the de Sitter cosmological horizon and (ii) in Schwarzschild--de Sitter spacetime, in the Gibbons-Hawking vacuum, which describes thermal fluxes of radiation emanating from both the hole and the cosmological horizons, respectively, where $\ensuremath{\Lambda}$ is the cosmological constant and M is the black hole mass. After performing the field quantization in each of the above spacetimes, we obtain the response rates at the tree level in terms of an infinite sum of zero-energy field modes possessing all possible angular momentum quantum numbers. In the case of de Sitter spacetime, this formula is worked out and a closed, analytical form is obtained. In the case of Schwarzschild--de Sitter spacetime such a closed formula could not be obtained, and a numerical analysis is performed. We conclude, in particular, that ${R}^{\mathrm{dS}}{(a}_{0},\ensuremath{\Lambda})$ and ${R}^{\mathrm{SdS}}{(a}_{0},\ensuremath{\Lambda},M)$ do not coincide in general, but tend to each other when $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Lambda}}0$ or ${a}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}.$ Our results are also contrasted and shown to agree (in the proper limits) with related ones in the literature.

Since the black hole and cosmological horizons in the de Sitter (dS) spacetime with the Reissner–Nordström (RN) black hole are not independent with each other, which is caused by the gravitational effect, the interplay between two horizons should be considered. Based on this, by introducing the interactive entropy the RN–dS spacetime is analogous to a thermodynamic system with various thermodynamic quantities, in which the laws of thermodynamics still hold on. In our work, the thermodynamic properties of the RN–dS spacetime are mapped out in the induced phase space, which are similar to that in AdS black holes. The phase transition of the RN–dS spacetime between the high-potential and the low-potential black hole phases is observed. Compared with an ordinary thermodynamic system, the similar behaviors about the Joule–Thomson expansion and the critical exponents are also checked out. Finally, the scalar curvatures of two existent phases are presented to reveal the underlying microstructure and nature of phase transition in the RN–dS spacetime, which opens a new window to investigate the dS spacetime with black holes from an observational perspective.

The statement is often made that the second quantized Hamiltonian for a system of noninteracting particles in an external weak electromagnetic field gives rise essentially to a one-particle problem, to which there corresponds a dressed vacuum different from the bare one. In this paper we implement that statement by explicitly constructing the dressed vacuum, together with the quasiparticle creation and annihilation operators associated with the one-particle problem. The process of diagonalizing the Hamiltonian is illustrated step by step in a simple model.

We carefully consider the Shapiro time delay due to black holes and shockwaves in de Sitter spacetime and study the implications for causality. We discuss how causality conditions of AdS and flat spacetime can be applied in de Sitter spacetime, using spatial shifts measured on the boundary to define ‘fastest null geodesics’ and taking into account the ‘stretching’ of the de Sitter Penrose diagram. We consider the propagation of a massless spin-1 field with a non-minimal coupling in a de Sitter shockwave background as an illustrative example. We also briefly discuss connections to the average null energy condition.

We study the scalar radiation emitted by a source orbiting a Schwarzschild--anti--de Sitter black hole in circular geodesics. We obtain the emitted power using quantum field theory in curved spacetimes at tree level with reflective boundary conditions at infinity. We compare our results with the ones obtained in Schwarzschild and Schwarzschild--de Sitter ($\mathrm{\ensuremath{\Lambda}}>0$) spacetimes. In the Schwarzschild--de Sitter spacetime we observe an enhancement of the emitted power associated to the lower multipole modes, when compared with the Schwarzschild case. In contrast, for the Schwarzschild--anti--de Sitter spacetime, the enhancement is rather of the higher multipole modes.

The possibility of cooperative spontaneous two-photon emission of an extended radiators system and the influence of the external thermal electromagnetic field on the spontaneous emission rate, in such a system, are investigated. It is concluded that, in an external electromagnetic field, the two-photon cooperative emission rate increases significantly. The importance of this effect on the emission of gamma rays from inverted long-lived isomers triggered by X-ray thermal fields, is emphasized.

Verification of Nuclear Magnetic Resonance Characterization of Traditional Homeopathically Manufactured Metal (Cuprum metallicum) and Plant (Gelsemium sempervirens) Medicines and Controls.

Bernstein and Lee and, independently, Meyer and Schiff have recently published calculations of the neutrino electromagnetic form factor, obtaining results differing by a finite constant term. This difference can be traced back to how the $W$-meson contribution is regularized: The Bernstein-Lee calculation is gauge-invariant at every step, while Meyer and Schiff simply impose over-all neutrino charge neutrality at the end. The $\ensuremath{\xi}$-limiting process in addition sums a class of electromagnetic radiative corrections and assigns the value $\mathrm{ln}{\ensuremath{\alpha}}^{\ensuremath{-}1}$ to the logarithmically divergent term in the $W$-meson contribution. Since the finite term, which is almost comparable to $\mathrm{ln}{\ensuremath{\alpha}}^{\ensuremath{-}1}$ in magnitude, is not fixed by the $\ensuremath{\xi}$-limiting method, the neutrino form factor has actually been determined only to order of magnitude by this method. For this reason and because the $W$ mass is large (or infinite), we have determined the largest part of the neutrino form factor from the charged lepton contribution using a guage-invariant direct-interaction theory. This is obtained, without further calculation, from the photon vacuum polarization. The ${\ensuremath{\nu}}_{e}$ charge radius thus measures the same integral that appears in the perturbation-theory calculation of ${{Z}_{3e}}^{\frac{1}{2}}$, the charge renormalization in quantum electrodynamics.

The entropy of a free scalar field is calculated in the Reissner–Nordström–(anti-)de Sitter spacetimes. Due to the presence of the cosmological horizon in the Reissner–Nordström–de Sitter spacetime, we introduce a cutoff at the cosmological horizon, besides the cutoff at the horizon of black holes in the brick wall model. The entropy is found to be the sum of two terms, which are proportional to the area of the cosmological horizon and of black hole horizon, respectively. In the Reissner–Nordström–anti-de Sitter spacetime the contribution of the anti-de Sitter background to the entropy of scalar fields vanishes when an infinite volume is taken. The entropy of scalar fields is also evaluated in some special backgrounds described by solutions of Einstein–Maxwell equations with a cosmological constant, such as the cold black holes, lukewarm black holes, ultracold solutions, a naked singularity in de Sitter space, and the de Sitter space. The physical meaning of some results is briefly discussed.

Entropy of massive quantum fields in de Sitter space–time

We investigate Schwinger scalar pair production in a constant electromagnetic field in de Sitter (dS) spacetime. We obtain the pair production rate, which agrees with the Hawking radiation in the limit of zero electric field in dS. The result describes how a cosmic magnetic field affects the pair production rate. In addition, using a numerical method we study the effect of the magnetic field on the induced current. We find that in the strong electromagnetic field the current has a linear response to the electric and magnetic fields, while in the infrared regime, is inversely proportional to the electric field and leads to infrared hyperconductivity.

In this paper, we overview the early hypotheses on superconductivity in the models of the electron, and summarize the results of our research on the structure of the electron on the basis of general solutions to the dynamical equations of Nonlinear Electrodynamics minimally coupled to Gravity (NED-GR), which include regular solutions describing the electrically charged spinning solitons in a self-consistent way and without additional assumptions and special constraints on the relation between an electromagnetic field and gravity. Their nonlinear electromagnetic fields are governed by the NED-GR source-free equations for electromagnetic field, while the gravitational fields are generated by stress-energy tensors of their own electromagnetic fields. The basic constituent of these objects, defined unambiguously by the algebraic structure of a stress-energy tensor for an electromagnetic field, [Formula: see text], and spacetime symmetry, is the equatorial de Sitter vacuum disk which has zero magnetic induction, behaves as a perfect conductor and an ideal diamagnetic and is surrounded by the superconducting ring current. For the electron, the diameter of the de Sitter disk equals its Compton wavelength. The superconducting ring current, determined by the exact solution to the NED-GR field equations, equals 79,277 A and presents the intrinsic non-dissipative source of the electromagnetic field of the electron providing its in principle unlimited life time. Internal structure of the electron allows to suggest a certain explanation for appearance of the minimal length scale in the purely electromagnetic annihilation reaction [Formula: see text].