Relativistic Electrodynamics Research Articles

High field X-ray laser physics

High field X-ray laser physics

Polarization of accreting X-ray pulsars. I. A new model

ABSTRACT A new window is opening in high-energy astronomy: X-ray polarimetry. With many missions currently under development and scheduled to launch as early as 2021, observations of the X-ray polarization of accreting X-ray pulsars will soon be available. As polarization is particularly sensitive to the geometry of the emission region, the upcoming polarimeters will shed new light on the emission mechanism of these objects, provided that we have sound theoretical models that agree with current spectroscopic and timing observation and that can make predictions of the polarization parameters of the emission. We here present a new model for the polarized emission of accreting X-ray pulsars in the accretion column scenario that for the first time takes into account the macroscopic structure and dynamics of the accretion region and the propagation of the radiation towards the observer, including relativistic beaming, gravitational lensing, and quantum electrodynamics. In this paper, we present all the details of the model, while in a companion paper, we apply our model to predict the polarization parameters of the bright X-ray pulsar Hercules X-1.

Vacuum polarization and finite-nuclear-size effects in the two-photon decay of hydrogenlike ions

The total two-photon decay rate of hydrogen-like ions is studied using relativistic quantum electrodynamics. In particular, we analyse how finite nuclear size and QED vacuum polarization corrections affect the decay rate. To calculate these corrections, a finite basis set method based on $B$-splines is used for the generation of quasi-complete atomic spectra and, hence, of the relativistic Green's function. By making use of this $B$-spline approach, high precision calculations have been performed for the $2s_{1/2} \to 1s_{1/2} + 2\gamma$ and $2p_{1/2} \to 1s_{1/2} + 2\gamma$ decay of hydrogen-like ions along the entire isoelectronic sequence. The results of these calculations show that both, QED and finite nuclear size effects, are comparatively weak for the $2s_{1/2} \to 1s_{1/2} + 2\gamma$ transition. In contrast, they are much more pronounced for the $2p_{1/2}\to 1s_{1/2} + 2\gamma$ decay, where, for hydrogen-like Uranium, the decay rate is reduced by 0.484% due to the finite nuclear size and enhanced by 0.239% if the vacuum polarization is taken into account.

Electromagnetic dual Einstein-Maxwell-scalar models

Electromagnetic duality is discussed in the context of Einstein-Maxwell-scalar (EMS) models including axionic-type couplings. This family of models introduces two non-minimal coupling functions f(ϕ) and g(ϕ), depending on a real scalar field ϕ. Interpreting the scalar field as a medium, one naturally defines constitutive relations as in relativistic non-linear electrodynamics. Requiring these constitutive relations to be invariant under the SO(2) electromagnetic duality rotations of Maxwell’s theory, defines 1-parameter, closed duality orbits in the space of EMS models, connecting different electromagnetic fields in “dual” models with different coupling functions, but leaving both the scalar field and the spacetime geometry invariant. This mapping works as a solution generating technique, extending any given solution of a specific model to a (different) solution for any of the dual models along the whole duality orbit. We illustrate this technique by considering the duality orbits seeded by specific EMS models wherein solitonic and black hole solutions are known. For dilatonic models, specific rotations are equivalent to S-duality.

Discrete phase space, relativistic quantum electrodynamics, and a non-singular Coulomb potential

This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent relativistic quantum electrodynamics, the corresponding Feynman diagrams and [Formula: see text]-matrix elements are derived. In the special case of electron–electron scattering (Møller scattering), the explicit second-order element [Formula: see text] is deduced. Moreover, assuming the slow motions for two external electrons, the approximation of [Formula: see text] yields a divergence-free Coulomb potential.

Accurate deuterium spectroscopy and comparison with ab initio calculations

We present accurate measurements of the quadrupole S(3) and S(4) transitions of the ${\mathrm{D}}_{2}\phantom{\rule{4pt}{0ex}}2\ensuremath{-}0$ band. Self-perturbed spectra were collected in a wide pressure range with a cavity ring-down spectrometer linked to an optical frequency comb. The results of ab initio quantum scattering calculations were incorporated into the line-shape analysis which was performed using the Hartmann-Tran profile. This approach allowed us to mitigate the collisional systematics and to reach a 900-kHz accuracy of the transition frequencies, which represents a 30-fold improvement compared to previously available data. We also compare our findings with newly calculated transition frequencies that include relativistic and quantum electrodynamics corrections up to ${\ensuremath{\alpha}}^{7}$. The differences between theoretical and experimental values for the transition frequencies are 2.2 MHz and 3.3 MHz for the S(3) and S(4) transitions, respectively.

Preface

The 21st International Meeting Physical Interpretations of Relativity Theory (PIRT 2019) was held at the Bauman Moscow State Technical University, Moscow, Russia from July 1 to July 5, 2019. The conference has been held at Imperial College in London since 1988. Since 2003, the conference has been held at BMSTU once every two years. The main organizers are BMSTU, Liverpool University and the Russian Academy of Sciences.The major goal and feature of the conference were the discussion of modern generalizations of the relativity theory, its observed consequences, experimental verification of the relativity theory, methods for recording gravitational waves, effects of relativistic electrodynamics and moving-media optics, astrophysical observations and space experiments.The working languages of the conference were Russian and English, simultaneous interpretation of all reports was carried out. Previously abstracts of all the reports had been published.List of Conference Photographs, International Organizing Committee of PIRT-2019, Academician Committee of PIRT-2019 (International Advisory Council) are available in this PDF.

Striped Blandford/Znajek jets from advection of small-scale magnetic field

ABSTRACT Black hole – accretion disc systems are the central engines of relativistic jets from stellar to galactic scales. We numerically quantify the unsteady outgoing Poynting flux through the horizon of a rapidly spinning black hole endowed with a rotating accretion disc. The disc supports small-scale, concentric, flux tubes with zero net magnetic flux. Our general relativistic force-free electrodynamics simulations follow the accretion on to the black hole over several hundred dynamical time-scales in 3D. For the case of counter-rotating accretion discs, the average process efficiency reaches up to 〈ϵ〉 ≈ 0.43, compared to a stationary energy extraction by the Blandford/Znajek process. The process efficiency depends on the cross-sectional area of the loops, i.e. on the product l × h, where l is the radial loop thickness and h its vertical scale height. We identify a strong correlation between efficient electromagnetic energy extraction and the quasi-stationary setting of ideal conditions for the operation of the Blandford/Znajek process (e.g. optimal field line angular velocity and fulfillment of the so-called Znajek condition). Remarkably, the energy extraction operates intermittently (alternating episodes of high and low efficiency) without imposing any large-scale magnetic field embedding the central object. Scaling our results to supermassive black holes, we estimate that the typical variability time-scale of the system is of the order of days to months. Such time-scales may account for the longest variability scales of TeV emission observed, e.g. in M87.

Energies and emission strengths of Kα X-rays from iodine and gold with multiply ionized L shell

The energies and rates of Kα X-ray satellites due to 1s − 2p transitions in iodine and gold with one to multiple vacancies in the L shell are computed using Multi-Configuration Dirac Fock wavefunctions with the inclusion of relativistic and quantum electrodynamics corrections. The calculations have been carried out for I1+ to I6+ with spectator vacancies in the 2p shell and Au1+ to Au8+ with filled and empty 2s shell along with vacancies in the 2p shell. As existing data on the X-ray emission from low ionized iodine and gold are confined to single inner shell vacancy, direct comparison of the present results on the various radiative transitions from iodine and gold with a single vacancy in the K shell, variously ionized L shell and no vacancy in any other shells is possible only for the two well known Kα 1 and Kα 2 diagram lines. Hence to substantiate the reliability of the current results through one to one comparison with existing data on the 1s − 2p transitions, calculations have also been performed on the radiative decay of H-, He-, Be-, and F-like gold with singly ionized 1s , closed 2s , multiply ionized 2p and rest of the shells open for which semi-relativistic data exist. In addition to providing additional check on the reliability of the computed results, this comparison also tries to analyze the impact of higher order relativistic corrections on the K X-ray energies and rates. The intrinsic variations of transition properties with degree of ionization have been analyzed.

Rotation and Spin and Position Operators in Relativistic Gravity and Quantum Electrodynamics

First, we examine how spin is treated in special relativity and the necessity of introducing spin supplementary conditions (SSC) and how they are related to the choice of a center-of-mass of a spinning particle. Next, we discuss quantum electrodynamics and the Foldy–Wouthuysen transformation which we note is a position operator identical to the Pryce–Newton–Wigner position operator. The classical version of the operators are shown to be essential for the treatment of classical relativistic particles in general relativity, of special interest being the case of binary systems (black holes/neutron stars) which emit gravitational radiation.

Numerical Study of Voltage-Gated Ca2+ Transport Irradiated by Terahertz Electromagnetic Wave

This paper simulates Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> transmembrane transport through voltage-gated Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> channels in response to terahertz electromagnetic irradiation. The active transport of Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> ions is taken into considerations in the Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> transport. Temperature variations due to terahertz electromagnetic loss in physiological medium are simulated. The electromagnetic interaction between terahertz fields and physiological mobile ions at the cellular level is deduced from relativistic electrodynamics. It shows that effects of 0.1 ~ 3 THz electromagnetic fields on cell mobile ions are primarily due to effects of electric fields, and effects of magnetic fields at the cellular level are insignificant. In addition, numerical simulation reveals that terahertz irradiation causes vibration of membrane potential, which is able to activate voltage-gated Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> channels. Besides, bioeffects of terahertz frequency, irradiation duration and electric intensity on the increment of intracellular Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> concentration due to activation of voltage-gated Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> channels are revealed. Meanwhile, numerical results show that temperature rises are inconsequential in the case of different irradiation parameters, indicating the non-thermal bioeffects of voltage-gated Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> transmembrane transport due to terahertz irradiation. Furthermore, the results also reveal that thermal bioeffect can be significant if the irradiation duration is raised long enough for high-dose terahertz irradiation. The numerical simulations lay the basis for understanding the bioeffects of terahertz irradiation on Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> transmembrane transport and pave the way for further exploration in modulation of intracellular Ca <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> concentration with terahertz electromagnetic wave.

Relativistic Classical Mechanics and Electrodynamics

This book presents classical relativistic mechanics and electrodynamics in the Feynman-Stueckelberg event-oriented framework formalized by Horwitz and Piron. The full apparatus of classical analytical mechanics is generalized to relativistic form by replacing Galilean covariance with manifest Lorentz covariance and introducing a coordinate-independent parameter ���� to play the role of Newton's universal and monotonically advancing time. Fundamental physics is described by the ����-evolution of a system point through an unconstrained 8D phase space, with mass a dynamical quantity conserved under particular interactions. Classical gauge invariance leads to an electrodynamics derived from five ����-dependent potentials described by 5D pre-Maxwell field equations. Events trace out worldlines as ���� advances monotonically, inducing pre-Maxwell fields by their motions, and moving under the influence of these fields. The dynamics are governed canonically by a scalar Hamiltonian that generates evolution of a 4D block universe defined at ���� to an infinitesimally close 4D block universe defined at ����+��������. This electrodynamics, and its extension to curved space and non-Abelian gauge symmetry, is well-posed and integrable, providing a clear resolution to grandfather paradoxes. Examples include classical Coulomb scattering, electrostatics, plane waves, radiation from a simple antenna, classical pair production, classical CPT, and dynamical solutions in weak field gravitation. This classical framework will be of interest to workers in quantum theory and general relativity, as well as those interested in the classical foundations of gauge theory.

Effect of Coulomb screening on the discrete scale invariance of quasibound states in three-dimensional topological semimetals

We study the energy spectrum of Weyl fermions in a topological semimetal in the presence of a central charged impurity. When the strength of the charge exceeds a critical value, an infinite family of quasibound states appear that show characteristic signatures of discrete scale invariance. The invariance is broken by the presence of screening or a finite mass. If these terms are small enough the quasibound states still exist, but there can be perturbations of the shallowest quasibound states. These special quasibound states manifest themselves in the local density of states as well as the relative phase, which can be observed by scanning tunneling microscopy. Such effects that are usually associated with the relativistic quantum electrodynamics of strong fields become observable in topological materials.

Beyond Born−Oppenheimer: A canonical perspective

By using the classic Lennard-Jones potential as reference, inverse canonical transformations allow for the accurate generation of post Born−Oppenheimer potentials in the ground and excited electronic states for H2, He dimer, LiH, CH+, Mg2, HF, and OH radical. The two parameters in the reference Lennard-Jones potential are set to one. The studied potentials include corrections for adiabatic, nonadiabatic, relativistic, and quantum electrodynamics effects. The relative error in the generated potentials are less than 0.01. Application of canonical approaches with the algebraic Lennard-Jones potential accurately reproduces the best post Born−Oppenheimer potential curves of pairwise interatomic interactions.

Computation of rovibronic resonances of molecular hydrogen: EFΣg+1 inner-well rotational states

Selected states of the $EF\ ^1\Sigma_\mathrm{g}^+$ electronic manifold of the hydrogen molecule are computed as resonances of the four-body problem. Systematic improvement of the basis representation for the variational treatment is achieved through an energy-tracking optimization procedure. The resulting non-relativistic energy is converged within a few nano Hartree, while the predissociative width is found to be negligible at this level of accuracy. The four-particle non-relativistic energies are appended with relativistic and quantum electrodynamics corrections which close the gap between the experimental observations and earlier theoretical work.

Electrodynamic formulation of special relativity from the first postulate

This work presents the form that the special theory of relativity takes when only the first postulate and the properties of homogeneity and isotropy of space and time are considered valid. The transformations of Lorentz coordinates are obtained in terms of a universal constant parameter k, developing from these the relativistic kinematics, dynamics and electrodynamics and their respective invariances before these transformations.

Benchmarking Theory with an Improved Measurement of the Ionization and Dissociation Energies of H_{2}.

The dissociation energy of H_{2} represents a benchmark quantity to test the accuracy of first-principles calculations. We present a new measurement of the energy interval between the EF ^{1}Σ_{g}^{+}(v=0,N=1) state and the 54p1_{1} Rydberg state of H_{2}. When combined with previously determined intervals, this new measurement leads to an improved value of the dissociation energy D_{0}^{N=1} of ortho-H_{2} that has, for the first time, reached a level of uncertainty that is 3 times smaller than the contribution of about 1MHz resulting from the finite size of the proton. The new result of 35 999.582 834(11) cm^{-1} is in remarkable agreement with the theoretical result of 35 999.582 820(26) cm^{-1} obtained in calculations including high-order relativistic and quantum-electrodynamics corrections, as reported in the following Letter [M. Puchalski, J. Komasa, P. Czachorowski, and K. Pachucki, Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003]. This agreement resolves a recent discrepancy between experiment and theory that had hindered a possible use of the dissociation energy of H_{2} in the context of the current controversy on the charge radius of the proton.

A global potential energy surface for H3+

ABSTRACTA globally correct potential energy surface (PES) for the molecular ion is presented. The Born-Oppenheimer (BO) ab initio grid points of Pavanello et al. [J. Chem. Phys. 136, 184303 (2012)] are refitted as BOPES75K, which reproduces the energies below dissociation with a root mean square deviation of 0.05 cm−1; points between dissociation and 75,000 cm−1 are reproduced with the average accuracy of a few wavenumbers. The new PES75K+ potential combines BOPES75K with adiabatic, relativistic and quantum electrodynamics (QED) surfaces to provide the most accurate representation of the global potential to date, overcoming the limitations on previous high accuracy PESs near and above dissociation. PES75K+ can be used to provide predictions of bound rovibrational energy levels with an accuracy of approaching 0.1 cm−1. Calculation of rovibrational energy levels within PES75K+ suggests that the non-adiabatic correction remains a limiting factor. The PES is also constructed to give the correct asymptotic limit making it suitable for use in studies of the prototypical chemical reaction. An improved dissociation energy for is derived as cm−1.

On solutions for a system of equations of relativistic electrodynamics

The possibility of applying the homotopy (deformation) method to studying the invariance of extremals for a generalized system of equations of relativistic electrodynamics is considered. This approach allows to investigate the stability of extremals for the action functional.

Accurate wavenumber measurements for the S0(0), S0(1), and S0(2) pure rotational Raman lines of D2

AbstractWe present accurate measurements for the wavenumbers of the S0(0), S0(1), and S0(2) pure rotational Raman lines in D2. Our measurements improve the accuracy of the previously available experimental data by an order of magnitude. They also show complete agreement with the state‐of‐the‐art ab initio calculations of the D2 rotational splitting, which include both relativistic and Quantum electrodynamics (QED) corrections.