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Polar organic molecules form spontaneous polarization in vacuum-deposited films by permanent dipole orientations in the films, originating from the molecule's potential ability to align itself on the film surface during deposition. This study focuses on developing polar molecules that exhibit spontaneous orientation polarization (SOP) and possess a high surface potential. In the proposed molecular design, a hexafluoropropane (6F) unit facilitates spontaneous molecular orientation to align the permanent dipoles, and a phthalimide unit induces strong molecular polarization. Furthermore, the introduction of phthalimides into the molecular backbone raises the glass transition temperature of the molecules, leading to the suppression of molecular mobility on the film surface during film deposition and an improvement in the dipole orientation. The resulting surface potential slope is approximately 280 mV nm−1 without substrate temperature control. Furthermore, this work proposes a method using position isomers as a design strategy to tune the SOP polarity. The substitution position of the strong polar units influences the direction of the total molecular dipoles and affects the SOP polarity of the 6F-based molecules. The proposed molecular designs in this study provide wide tunability of the SOP intensity and polarity, which contributes to highly efficient organic optoelectronic and energy-harvesting devices. Polar organic molecules form spontaneous polarization in vacuum-deposited films originating from the molecule's potential ability to align itself on the film surface during deposition. Here, the author incorporates fluoroalkyl and phthalimide units to the molecular backbone to improve spontaneous molecular orientation facilitating strong polarization in vacuum deposited films. [ABSTRACT FROM AUTHOR]

We investigated Einstein–Gauss–Bonnet (EGB) 4D massive gravity coupled to nonlinear electrodynamics (NED) in an anti-de Sitter (AdS) background and found an exact magnetically charged black hole solution. The metric function was analyzed for different values of massive gravity parameters. The first law of black hole thermodynamics and generalized Smarr formula were verified, where we treated the cosmological constant as thermodynamic pressure. We defined vacuum polarization as the conjugate to NED parameter. To analyze the local stability of the black hole, we computed specific heat. We investigated the van der Waals-like/re-entrant phase transition of the black holes and estimated the critical points. We observed small black hole (SBH)/large black hole (LBH) and SBH/intermediate black hole (IBH)/LBH phase transitions. The Joule–Thomson coefficient, inversion, and isenthalpic curves were discussed. Finally, the minimum inversion temperature and the corresponding event horizon radius were obtained using numerical techniques. [ABSTRACT FROM AUTHOR]

One of the fundamental goals of particle physics is to gain a microscopic understanding of the strong interaction. Electromagnetic form factors quantify the structure of hadrons in terms of charge and magnetization distributions. While the nucleon structure has been investigated extensively, data on hyperons are still scarce. It has recently been demonstrated that electron-positron annihilations into hyperon-antihyperon pairs provide a powerful tool to investigate their inner structure. We present a method useful for hyperon-antihyperon pairs of different types which exploits the cross section enhancement due to the effect of vacuum polarization at the J/ψ resonance. Using the 10 billion J/ψ events collected with the BESIII detector, this allows a precise determination of the hyperon structure function. The result is essentially a precise snapshot of the Λ ¯ Σ 0 (Λ Σ ¯ 0 ) transition process, encoded in the transition form factor ratio and phase. Their values are measured to be R = 0.860 ± 0.029(stat.) ± 0.015(syst.), Δ Φ Λ ¯ Σ 0 = (1.011 ± 0.094 (stat.) ± 0.010 (syst.)) r a d and Δ Φ Λ Σ ¯ 0 = (2.128 ± 0.094 (stat.) ± 0.010 (syst.)) r a d . Furthermore, charge-parity (CP) breaking is investigated in this reaction and found to be consistent with CP symmetry. Investigating the inner structure of baryons is important to further our understanding of the strong interaction. Here, the BESIII Collaboration extracts the absolute value of the ratio of the electric to magnetic form factors and its relative phase for e + e − → J/ψ → ΛΣ decays, enhancing the signal thanks to the vacuum polarisation effect at the J/ψ peak. [ABSTRACT FROM AUTHOR]

The vacuum polarization effect of a massive scalar field near the point -like source is considered. The corresponding interaction is introduced within a technique of self-adjoint extension of the Laplace operator. This method has been widely discussed within the framework of quantum mechanics. We propose to use it to investigate vacuum field effects. This approach allows computing the renormalized Hadamard function and the renormalized vacuum energy density for massive real scalar field with minimal curvature coupling. The dependence of the vacuum polarization effect upon the fields's mass is analyzed. [ABSTRACT FROM AUTHOR]

We study Einstein's gravity in AdS space coupled to nonlinear electrodynamics. Thermodynamics in extended phase space of magnetically charged black holes is investigated. We compute the metric and mass functions and their asymptotics, showing that black holes may have one or two horizons. The metric function is regular, f (0) = 1 , and corrections to the Reissner–Nordström solution are in the order of O (r − 3) when the Schwarzschild mass is zero. We prove that the first law of black hole thermodynamics and the generalized Smarr relation hold. The magnetic potential and vacuum polarization conjugated to coupling are computed and depicted. We calculate the Gibbs free energy and the heat capacity showing that first-order and second-order phase transitions take place. [ABSTRACT FROM AUTHOR]

The second-order differential equation for the Uehling potential is derived explicitly. The right side of this differential equation is a linear combination of the two Macdonald's functions K 0 (b r) and K 1 (b r) . This central potential is of great interest in many QED problems, since it describes the lowest order correction for vacuum polarization in few- and many-electron atoms, ions, muonic and bi-muonic atoms/ions as well as in other similar systems. [ABSTRACT FROM AUTHOR]

The multi-configuration Dirac–Hartree–Fock method is employed to investigate the Mα transitions of He-like to C-like Co ions. This study encompasses various parameters, such as energy levels, wavelengths, transition rates, oscillator strengths, and line strengths. The Breit interaction, vacuum polarization, and self-energy corrections were included in the computation of energy levels. The computed results we obtained align well with both experimental and theoretical findings. The differences for most energy levels, transition wavelengths, and oscillator strengths are all below 0.6%, 0.8%, and 20%, respectively. The uncertainty estimation method of the transitions of line strength is evaluated using quantitative and qualitative evaluation methods. The resulting accurate and consistent MCDHF data are expected to be useful for theoretical research on cobalt ions. [ABSTRACT FROM AUTHOR]

We report the implementation of effective quantum electrodynamics (QED) potentials for all-electron four-component relativistic molecular calculations using the DIRAC code. The potentials are also available for two-component calculations, being properly picture-change transformed. The latter point is important; we demonstrate through atomic calculations that picture-change errors are sizable. Specifically, we have implemented the Uehling potential [E. A. Uehling, Phys. Rev. 48, 55 (1935)] for vacuum polarization and two effective potentials [P. Pyykkö and L.-B. Zhao, J. Phys. B: At., Mol. Opt. Phys. 36, 1469 (2003) and V. V. Flambaum and J. S. M. Ginges, Phys. Rev. A 72, 052115 (2005)] for electron self-energy. We provide extensive theoretical background for these potentials, hopefully reaching an audience beyond QED specialists. We report the following sample applications: (i) We first confirm the conjecture of P. Pyykkö that QED effects are observable for the AuCN molecule by directly calculating ground-state rotational constants B0 of the three isotopomers studied by microwave spectroscopy; QED brings the corresponding substitution Au–C bond length rs from 0.23 to 0.04 pm agreement with experiment. (ii) In regard to spectroscopic constants of van der Waals dimers M2 (M = Hg, Rn, Cn, Og), QED induces bond length expansions on the order of 0.15(0.30) pm for row 6(7) dimers. (iii) We confirm that there is a significant change of valence s population of Pb in the reaction PbH4 → PbH2 + H2, which is thereby a good candidate for observing QED effects in chemical reactions, as proposed in [K. G. Dyall et al., Chem. Phys. Lett. 348, 497 (2001)]. We also find that whereas in PbH4 the valence 6s1/2 population resides in bonding orbitals, it is mainly found in nonbonding orbitals in PbH2. QED contributes 0.32 kcal/mol to the reaction energy, thereby reducing its magnitude by −1.27%. For corresponding hydrides of superheavy flerovium, the electronic structures are quite similar. Interestingly, the QED contribution to the reaction energy is of quite similar magnitude (0.35 kcal/mol), whereas the relative change is significantly smaller (−0.50%). This curious observation can be explained by the faster increase in negative vacuum polarization over positive electron self-energy contributions as a function of nuclear charge. [ABSTRACT FROM AUTHOR]

Cosmic censorship protects the outside world from black hole singularities and paves the way for assigning entropy to gravity at the event horizons. We point out a tension between cosmic censorship and the quantum backreacted geometry of Schwarzschild black holes, induced by vacuum polarization and driven by the conformal anomaly. A similar tension appears for the Weyl curvature hypothesis at the Big Bang singularity. We argue that the requirement of exact conformal symmetry resolves both conflicts and has major implications for constraining the set of fundamental constituents of the Standard Model. [ABSTRACT FROM AUTHOR]

Magnetars, the most strongly magnetized neutron stars, are among the most promising targets for X-ray polarimetry. Imaging X-ray Polarimetry Explorer (IXPE), the first satellite devoted to exploring the sky in polarized X-rays, has observed four magnetars to date. A proper interpretation of IXPE results requires the development of new atmospheric models that can take into proper account the effects of the magnetized vacuum on par with those of the plasma. Here we investigate the effects of mode conversion at the vacuum resonance on the polarization properties of magnetar emission by computing plane-parallel atmospheric models under varying conditions of magnetic field strength/orientation, effective temperature, and allowing for either complete or partial adiabatic mode conversion. Complete mode conversion results in a switch of the dominant polarization mode, from the extraordinary (X) to the ordinary (O) one, below an energy that decreases with increasing magnetic field strength, occurring at |$\approx 0.5\, \mathrm{keV}$| for a magnetic field strength of |$B=10^{14}\, \mathrm{G}$|⁠. Partial adiabatic mode conversion results in a reduced polarization degree when compared with a standard plasma atmosphere. No dominant mode switch occurs for |$B=10^{14}\, \mathrm{G}$|⁠ , while there are two switches for lower fields of |$B=3\times 10^{13}\, \mathrm{G}$|⁠. Finally, by incorporating our models in a ray-tracing code, we computed the expected polarization signal at infinity for different emitting regions on the star surface and for different viewing geometries. The observability of quantum electrodynamics signatures with IXPE and with future soft X-ray polarimeters as Rocket Experiment Demonstration of a Soft X-ray Polarimeter is discussed. [ABSTRACT FROM AUTHOR]

We present results for the short-distance window observable of the hadronic vacuum polarization contribution to the muon g – 2, computed via the time-momentum representation (TMR) in lattice QCD. A key novelty of our calculation is the reduction of discretization effects by a suitable subtraction applied to the TMR kernel function, which cancels the leading -behaviour at short distances. To compensate for the subtraction, one must substitute a term that can be reliably computed in perturbative QCD. We apply this strategy to our data for the vector current collected on ensembles generated with 2 + 1 flavours of O(a)-improved Wilson quarks at six values of the lattice spacing and pion masses in the range 130 – 420 MeV. Our estimate at the physical point contains a full error budget and reads = 68.85(14)stat (42)syst·10−10, which corresponds to a relative precision of 0.7%. We discuss the implications of our result for the observed tensions between lattice and data-driven evaluations of the hadronic vacuum polarization. [ABSTRACT FROM AUTHOR]

In this paper, we study the relationship between the Dirac–Fock model and the electron-positron Hartree–Fock model. We justify the Dirac–Fock model as a variational approximation of QED when the vacuum polarization is neglected and when the fine structure constant α is small and the velocity of light c is large. As a byproduct, we also prove, when α is small or c is large, the no-unfilled shells theory in the Dirac–Fock theory for atoms and molecules. The proof is based on some new properties of the Dirac–Fock model. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the vacuum expectation values of the field squared and the energy–momentum tensor associated to a charged massive scalar quantum field in a (1 + D) -dimensional de Sitter spacetime induced by a plate (flat boundary) and a carrying-magnetic-flux cosmic string. In our analysis, we admit that the flat boundary is perpendicular to the string, and the scalar field obeys the Robin boundary condition on the plate. In order to develop this analysis, we obtain the complete set of normalized positive-energy solutions of the Klein–Gordon equation compatible with the model setup. Having obtained these bosonic modes, we construct the corresponding Wightman function. The latter is given by the sum of two terms: one associated with the boundary-free spacetime, and the other induced by the flat boundary. Although we have imposed the Robin boundary condition on the field, we apply our formalism considering specifically the Dirichlet and Neumann boundary conditions. The corresponding parts have opposite signs. Because the analysis of bosonic vacuum polarization in boundary-free de Sitter space and in the presence of a cosmic string, in some sense, has been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way, closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions. We show that the conical topology due to the cosmic string enhances the boundary-induced vacuum polarization effects for both field squared and the energy–momentum tensor, compared to the case of a boundary in pure de Sitter spacetime. Moreover, the presence of a cosmic string and boundary induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is also investigated. [ABSTRACT FROM AUTHOR]

We study the back-reaction of fermion fields on the kink solution in one space and one time dimension. We employ a variational procedure to determine an upper limit for the minimum of the total energy. This energy has three contributions: the classical kink energy, the energy of valence fermions and the fermion vacuum polarization energy. The latter arises from the interaction of the kink with the Dirac sea and is required for consistency of the semi-classical expansion for the fermions. Earlier studies only considered the valence part and observed a substantial back-reaction. This was reflected by a sizable distortion of the kink profile. We find that this distortion is strongly mitigated when the Dirac sea is properly accounted for. As a result, the back-reaction merely produces a slight squeeze or stretch of the kink profile. [ABSTRACT FROM AUTHOR]

The equivalent representations for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment a μ HVP in the presence of the quark flavour thresholds are studied. Specifically, the explicit relations between the contributions given by the integration over a finite kinematic interval to a μ HVP expressed in terms of the hadronic vacuum polarization function, Adler function, and the R -ratio of electron–positron annihilation into hadrons are derived. It is shown that the quark flavour thresholds of the hadronic vacuum polarization function generate additional contributions to a μ HVP expressed in terms of the Adler function and the R -ratio and the explicit expressions for such contributions are obtained. The commonly employed dispersion relations, which bind together hadronic vacuum polarization function, Adler function, and R -ratio, are extended to account for the effects due to the quark flavour thresholds. The examined additional contributions due to the heavy quark thresholds to a μ HVP expressed in terms of the R -ratio appear to be quite sizable, that can be of a particular relevance for the data-driven method of assessment of the hadronic part of the muon anomalous magnetic moment. [ABSTRACT FROM AUTHOR]

The QED hadronic vacuum polarization function plays an important role in the determination of precision electroweak observables and of the anomalous magnetic moment of the muon. These contributions have been computed from data, by means of dispersion relations affecting the electron positron hadronic cross sections, or by first principle lattice-QCD computations in the Standard Model. Today there is a discrepancy between the two approaches for determining these contributions, which affects the comparison of the measurement of the anomalous magnetic moment of the muon with the theoretical predictions. In this article, we revisit the idea that this discrepancy may be explained by the presence of a new light gauge boson that couples to the first generation quark and leptons and has a mass below the GeV scale. We discuss the requirements for its consistency with observations and the phenomenological implications of such a gauge extension. [ABSTRACT FROM AUTHOR]

The QED hadronic vacuum polarization function plays an important role in the determination of precision electroweak observables and of the anomalous magnetic moment of the muon. These contributions have been computed from data, by means of dispersion relations affecting the electron positron hadronic cross sections, or by first principle lattice-QCD computations in the Standard Model. Today there is a discrepancy between the two approaches for determining these contributions, which affects the comparison of the measurement of the anomalous magnetic moment of the muon with the theoretical predictions. In this article, we revisit the idea that this discrepancy may be explained by the presence of a new light gauge boson that couples to the first generation quark and leptons and has a mass below the GeV scale. We discuss the requirements for its consistency with observations and the phenomenological implications of such a gauge extension. [ABSTRACT FROM AUTHOR]

A variational solution procedure is reported for the many-particle no-pair Dirac–Coulomb and Dirac–Coulomb–Breit Hamiltonians aiming at a parts-per-billion (ppb) convergence of the atomic and molecular energies, described within the fixed nuclei approximation. The procedure is tested for nuclear charge numbers from Z = 1 (hydrogen) to 28 (iron). Already for the lowest Z values, a significant difference is observed from leading-order Foldy–Woythusen perturbation theory, but the observed deviations are smaller than the estimated self-energy and vacuum polarization corrections. [ABSTRACT FROM AUTHOR]

Weber’s electrodynamics presents an alternative theory to the widely accepted Maxwell–Lorentz electromagnetism. It is founded on the concept of direct action between particles, and has recently gained some momentum through theoretical and experimental advancements. However, a major criticism remains: the lack of a comprehensive electromagnetic wave equation for free space. Our motivation in this research article is to address this criticism, in some measure, by deriving an electric wave equation from Weber’s electrodynamics based on the axiom of vacuum polarization. Although this assumption has limited experimental evidence and its validity remains a topic of debate among researchers, it has been shown to be useful in the calculation of various quantum mechanical phenomena. Based on this concept, and beginning with Weber’s force, we derive an expression which resembles the familiar electric field wave equation derived from Maxwell’s equations.

The increasing accuracy of current and planned experiments to measure the anomalous magnetic moment of the muon requires more precision and reliability of its theoretical calculation. For this purpose, we calculate the differential cross section for the process of annihilation of an electron-positron pair into two photons, one of which is virtual, accompanied by the emission of soft photons, taking into account radiative corrections of the order α2. The results obtained can be used to improve the accuracy of calculating the contribution of the hadron vacuum polarization to the muon anomalous moment. It is shown that all logarithmically amplified two-loop corrections can be easily found using modern theorems of soft and collinear factorizations and available one-loop results. [ABSTRACT FROM AUTHOR]

We report the development of an efficient method for calculating the number and characteristics of photons emitted by a vacuum polarized by overlapping focused laser pulses. The dependence of the signal on the focusing and polarization of pulses is studied and optimized, and the possibility of its detection on the XCELS multipetawatt facility is substantiated. [ABSTRACT FROM AUTHOR]

Within the framework of one-loop quantum gravity, we consider the vacuum polarization effect of the minimally-coupled massive scalar field near the infinitely-thin straight cosmic string. It is shown that the massive-field relative contribution to the renormalized vacuum mean of the energy density becomes negligible at a distance of several Compton lengths. [ABSTRACT FROM AUTHOR]

Eicheon properties are discussed. It is shown that the eicheon surface allows setting a boundary condition for the vacuum polarization and obtaining a solution describing the dark matter tail in the Milky Way Galaxy. That is, the dark matter in the Milky Way Galaxy is explained as the F-type of vacuum polarization, which could be treated as dark radiation. The model presented is spherically symmetric, but a surface density of a baryonic galaxy disk is taken into account approximately by smearing the disk over a sphere. This allows the reproduction of the large distance shape of the Milky Way Galaxy rotational curve. Andromeda Galaxy's rotational curve is also discussed. [ABSTRACT FROM AUTHOR]

Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e+e−→ π+π− channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for e+e−→ 3π by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and ρ–ω mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor η3π that generalizes the analog treatment of virtual and final-state photons in the 2π case. The global fit to the e+e−→ 3π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives a μ 3 π ≤ 1.8 GeV = 45.91 53 × 10 − 10 for the total 3π contribution to the anomalous magnetic moment of the muon, of which a μ FSR 3 π = 0.51 1 × 10 − 10 and a μ ρ − ω 3 π = − 2.68 70 × 10 − 10 can be ascribed to IB. We argue that the resulting cancellation with ρ–ω mixing in e+e−→ 2π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters Mω = 782.70(3) MeV, Mϕ = 1019.21(2) MeV, Γω = 8.71(3) MeV, and Γϕ = 4.27(1) MeV. [ABSTRACT FROM AUTHOR]

The muon Lamb shift (2 –2 is calculated in electron–muon helium atom on the basis of stochastic variational method. The basis wave functions of muonic helium are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation a computer code is written in the MATLAB system. The corrections to the nucleus structure, vacuum polarization, relativism and radiative corrections are taken into account by the perturbation theory. [ABSTRACT FROM AUTHOR]

In this paper, we study the processes of e+e− annihilation into two body final states, either two pseudoscalar mesons or one meson with a photon. The hadronic vacuum polarization form factors are calculated within the framework of resonance chiral theory in the energy region of E ≲ 2 GeV, with final state interactions taken into account. A joint analysis on the processes of e+e−→ π+π−, K+K−, K L 0 K S 0 , π0γ, and ηγ has been performed, and the latest experimental data are included. Based on the vacuum polarization form factors of these processes, we estimate their contributions to the lowest order of anomalous magnetic moment of the muon, (g – 2)μ. Combined with other contributions from hadronic vacuum polarization and other interactions from the standard model, the discrepancy between theoretical prediction and experimental measurement is ∆aμ = (24.1 ± 5.4) × 10−10, i.e., 4.5σ. [ABSTRACT FROM AUTHOR]

In this paper, we study the processes of e+e− annihilation into two body final states, either two pseudoscalar mesons or one meson with a photon. The hadronic vacuum polarization form factors are calculated within the framework of resonance chiral theory in the energy region of E ≲ 2 GeV, with final state interactions taken into account. A joint analysis on the processes of e+e−→ π+π−, K+K−, K L 0 K S 0 , π0γ, and ηγ has been performed, and the latest experimental data are included. Based on the vacuum polarization form factors of these processes, we estimate their contributions to the lowest order of anomalous magnetic moment of the muon, (g – 2)μ. Combined with other contributions from hadronic vacuum polarization and other interactions from the standard model, the discrepancy between theoretical prediction and experimental measurement is ∆aμ = (24.1 ± 5.4) × 10−10, i.e., 4.5σ. [ABSTRACT FROM AUTHOR]

In this paper, we compute the full vacuum polarization tensor in the fermion sector of Lorentz-violating quantum electrodynamics (QED). It turns out to be that even if we assume momentum routing invariance of the Feynman diagrams, it is not possible to fix all surface terms and find an ambiguity-free vacuum polarization tensor. The high- and low-energy limits of this tensor are obtained explicitly. In the high-energy limit, only c μ ν coefficients contribute to the result. In the low-energy limit, we find that Lorentz-violating-induced terms depend on b μ , c μ ν and g μ ν λ coefficients and vanish at p = 0. At small p , we succeeded to obtain implications for condensed matter systems, explicitly, for the Hall effect in Weyl semi-metals. [ABSTRACT FROM AUTHOR]

We study the backreaction of quantum fields induced through the vacuum polarization and the conformal anomaly on the collapse of a thin shell of dust. It is shown that the final fate of the collapse process depends on the physical properties of the shell, including its rest and gravitational masses. Investigating the conditions for the formation of black holes, we notice that quantum effects modify the geometry and structure of Schwarzschild space-time in such a way that black holes have two horizons, an inner and an outer horizon. If the gravitational mass of the shell is about that of an ordinary star, then in most cases, the semi-classical collapse will terminate in a singularity, and in general, quantum fluctuations are not strong enough to prevent the creation of the singularity. Although under certain conditions, it is possible to form a non-singular black hole, i.e., a regular black hole. In this way, the collapse stops at a radius much larger than the Planck length below the inner horizon, and the shell bounces and starts an expansion. [ABSTRACT FROM AUTHOR]

In grand-unified-theory-inspired SO (5) × U (1) X × SU (3) C gauge-Higgs unification (GHU) in the Randall–Sundrum warped spacetime, the W- and Z- couplings of all 4D fermion modes become nontrivial. The W - and Z -couplings of zero-mode quarks and leptons slightly deviate from those in the SM, and the couplings take the matrix form in the space of Kaluza–Klein (KK) states. In particular, the 4D couplings and mass spectra in the KK states depend on the Aharonov–Bohm phase θ H in the fifth dimension. Nevertheless there emerge three astonishing sum rules among those coupling matrices, which guarantees the finiteness of certain combinations of corrections to vacuum polarization tensors. We confirm by numerical evaluation that the equality in the sum rules holds with 5- to 7-digit accuracy. Based on the sum rules we propose improved oblique parameters in GHU. Oblique corrections due to fermion 1-loop diagrams are found to be small. [ABSTRACT FROM AUTHOR]

Weber's electrodynamics presents an alternative theory to the widely accepted Maxwell–Lorentz electromagnetism. It is founded on the concept of direct action between particles, and has recently gained some momentum through theoretical and experimental advancements. However, a major criticism remains: the lack of a comprehensive electromagnetic wave equation for free space. Our motivation in this research article is to address this criticism, in some measure, by deriving an electric wave equation from Weber's electrodynamics based on the axiom of vacuum polarization. Although this assumption has limited experimental evidence and its validity remains a topic of debate among researchers, it has been shown to be useful in the calculation of various quantum mechanical phenomena. Based on this concept, and beginning with Weber's force, we derive an expression which resembles the familiar electric field wave equation derived from Maxwell's equations. [ABSTRACT FROM AUTHOR]

We investigate the expectation value of the field squared for a charged scalar field in the Rindler spacetime with toroidally compact dimensions. The expectation values are compared for the Fulling-Rindler and Minkowski vacua. For general phases in the periodicity conditions on the field operator along compact dimensions, integral representations are provided for the difference of those expectation values. The vacuum expectation value of the field squared is an even periodic function of the magnetic flux enclosed by compact dimensions. Simple asymptotic expressions are given near the Rindler horizon and for small accelerations. We show that the mean field squared in the Fulling-Rindler vacuum is smaller than the respective expectation value for the Minkowski vacuum. [ABSTRACT FROM AUTHOR]

We propose a new set of model independent approximants adapted to the time momentum representation (TMR) of hadronic vacuum polarization (HVP) and its contribution to gμ– 2. They provide a way to extrapolate lattice QCD (LQCD) results obtained in an optimal time-region, to the full range required for an evaluation of the HVP contribution to gμ– 2. They offer as well a new way to confront LQCD results in restricted TMR regions, with the full contribution obtained from data driven determinations. [ABSTRACT FROM AUTHOR]

Lattice QCD calculations of the hadronic vacuum polarization (HVP) have reached a precision where the electromagnetic (e.m.) correction can no longer be neglected. This correction is both computationally challenging and hard to validate, as it leads to ultraviolet (UV) divergences and to sizeable infrared (IR) effects associated with the massless photon. While we precisely determine the UV divergence using the operator-product expansion, we propose to introduce a separation scale Λ ~ 400 MeV into the internal photon propagator, whereby the calculation splits into a short-distance part, regulated in the UV by the lattice and in the IR by the scale Λ, and a UV-finite long-distance part to be treated with coordinate-space methods, thereby avoiding power-law finite-size effects altogether. In order to predict the long-distance part, we express the UV-regulated e.m. correction to the HVP via the forward hadronic light-by-light (HLbL) scattering amplitude and relate the latter via a dispersive sum rule to γ∗γ∗ fusion cross-sections. Having tested the relation by reproducing the two-loop QED vacuum polarization (VP) from the tree-level γ∗γ∗→ e+e− cross-section, we predict the expected lattice-QCD integrand resulting from the γ∗γ∗→ π0 process. [ABSTRACT FROM AUTHOR]

The rapid progress of ultraintense laser technology provides a novel route to explore the quantum vacuum effect in the laboratory. Here, we propose using oblique collisions between an ultraintense pump laser and an x-ray probe laser to experimentally identify the quantum vacuum effect, where the change of the refraction properties including the refraction angle of the probe laser is taken as a detectable signature. The theoretical basis of the proposed scheme are analyzed in details, where a reasonable estimation of the scheme is given. To verify the proposed scheme, a series of two-dimensional particle-in-cell (PIC) simulations, with the vacuum polarization effect self-consistently taken into account, are carried out.

We formulate the Hartree–Fock method using a functional integral approach. Then we consider a nonperturbative component of the vacuum polarization. For the Dirac–Coulomb operator the renormalization flow of the vacuum polarization is calculated numerically. For the Hartree–Fock operator the polarization is obtained by integrating an appropriately rescaled flow. The text includes an approximate calculation of the vacuum polarization in Uranium. [ABSTRACT FROM AUTHOR]

Vacuum polarization of a scalar field on the short throat wormhole background is investigated. The scalar field is assumed to be massless, having an arbitrary coupling to the scalar curvature of spacetime. In addition, it is supposed that the field is in a thermal state with an arbitrary temperature. [ABSTRACT FROM AUTHOR]

This addendum provides results complementary to those obtained in [ J. Phys. G 49, 055001 (2022)]. Specifically, an equivalent form of the relation, which binds together the 'spacelike' kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment a μ HVP , is obtained. It is shown that the infrared limiting value of the 'spacelike' and 'timelike' kernel functions, which enter the representations for a μ HVP involving the Adler function and the R -ratio, is identical to the corresponding QED contribution to the muon anomalous magnetic moment of the preceding order in the electromagnetic coupling. The next-to-leading order contributions a μ HVP (3 b) (which includes the leptonic and hadronic insertions) and a μ HVP (3 c) (which includes the double hadronic insertion), are studied. The three kernel functions appearing in the representations for a μ HVP (3 b) , which involve the hadronic vacuum polarization function, Adler function, and the R -ratio, are presented for the cases of the electron and τ -lepton loop insertions. [ABSTRACT FROM AUTHOR]

In the framework of strong-field QED with x-steps, we study vacuum mean values of the current density and energy–momentum tensor of the quantized spinor field placed in the so-called L-constant electric background. The latter background can be, for example, understood as the electric field confined between capacitor plates, which are separated by a sufficiently large distance L. First, we reveal peculiarities of nonperturbative calculating of mean values in strong-field QED with x-steps in general and, in the L-constant electric field, in particular. We propose a new renormalization and volume regularization procedures that are adequate for these calculations. We find necessary representations for singular spinor functions in the background under consideration. With their help, we calculate the above mentioned vacuum means. In the obtained expressions, we show how to separate global contributions due to the particle creation and local ones due to the vacuum polarization. We demonstrate how these contributions can be related to the renormalized effective Heisenberg–Euler Lagrangian. [ABSTRACT FROM AUTHOR]

We study a quantum scalar field, with general mass and coupling to the scalar curvature, propagating on three-dimensional global anti-de Sitter space-time. We determine the vacuum and thermal expectation values of the square of the field, also known as the vacuum polarisation (VP). We consider values of the scalar field mass and coupling for which there is a choice of boundary conditions giving well-posed classical dynamics. We apply Dirichlet, Neumann and Robin (mixed) boundary conditions to the field at the space-time boundary. We find finite values of the VP when the parameter governing the Robin boundary conditions is below a certain critical value. For all couplings, the vacuum expectation values of the VP with either Neumann or Dirichlet boundary conditions are constant and respect the maximal symmetry of the background space-time. However, this is not the case for Robin boundary conditions, when both the vacuum and thermal expectation values depend on the space-time location. At the space-time boundary, we find that both the vacuum and thermal expectation values of the VP with Robin boundary conditions converge to the result when Neumann boundary conditions are applied, except in the case of Dirichlet boundary conditions. [ABSTRACT FROM AUTHOR]

Based on computational quantum field theory and solutions to the Dirac equation, we show how the vacuum's polarization density induced by strong external field can be calculated based on five independent methods. We compare these methods for a spatially reduced dimensional system and show that some approaches rely on energy renormalizations, energy cutoffs or periodic boundaries. We also illustrate the spatial implications of the breakdown of the linear superposition principle for extremely high intensity fields. A main focus of the article is to discuss future challenges for each approach that might motivate new theoretical and computational studies. [ABSTRACT FROM AUTHOR]

Dark matter in the Milky Way is explained by the F-type of vacuum polarization, which could represent dark radiation. A nonsingular solution for dark radiation exists in the presence of eicheon (i.e., black hole in old terminology) in the galaxy's center. The model is spherically symmetric, but an approximate surface density of a baryonic galaxy disk is taken into account by smearing the disk over a sphere. [ABSTRACT FROM AUTHOR]

Geometry and dynamical structure of emission regions in accreting pulsars are shaped by the interplay between gravity, radiation, and strong magnetic field, which significantly affects the opacities of a plasma and radiative pressure under such extreme conditions. Quantitative consideration of magnetic plasma opacities is therefore an essential ingredient of any self-consistent modelling of emission region structure of X-ray pulsars (XRPs). We present results of computations of the Rosseland and Planck mean opacities of a strongly magnetized plasma with a simple chemical composition, namely the solar hydrogen/helium mix. We consider all relevant specific opacities of the magnetized plasma including vacuum polarization effect and contribution of electron–positron pairs where the pair number density is computed in the thermodynamic equilibrium approximation. The magnetic Planck mean opacity determines the radiative cooling of an optically thin strongly magnetized plasma. It is by factor of three smaller than non-magnetic Planck opacity at |$k_{\rm B}T \lt 0.1\, E_{\rm cyc}$| and increases by a factor of 102–104 at |$k_{\rm B}T \gt 0.3\, E_{\rm cyc}$| due to cyclotron thermal processes. We propose a simple approximate expression which has sufficient accuracy for the magnetic Planck opacity description. We provide the Rosseland opacity in a tabular form computed in the temperature range 1–300 keV, magnetic field range 3 × 1010–1015 G, and a broad range of plasma densities. We demonstrate that the scattering on the electron–positron pairs increases the Rosseland opacity drastically at temperatures > 50 keV in the case of mass densities typical for accretion channel in XRPs. [ABSTRACT FROM AUTHOR]

The rigorous two-center approach based on the dual-kinetically balanced finite-basis-set expansion is applied to one-electron, heteronuclear diatomic Bi-Au, U-Pb, and Cf-U quasimolecules. The obtained 1 σ ground-state energies are compared with previous calculations, when possible. Upon analysis of three different placements of the coordinate system's origin in the monopole approximation of the two-center potential: (1) in the middle, between the nuclei, (2) in the center of the heavy nucleus, and (3) in the center of the light nucleus, a substantial difference between the results is found. The leading contributions of one-electron quantum electrodynamics (self-energy and vacuum polarization) are evaluated within the monopole approximation as well. [ABSTRACT FROM AUTHOR]

The theoretical foundations of relativistic electronic structure theory within quantum electrodynamics (QED) and the computational basis of the atomic structure code GRASP are briefly surveyed. A class of four-component basis set is introduced, which we denote the CKG-spinor set, that enforces the charge-conjugation symmetry of the Dirac equation. This formalism has been implemented using the Gaussian function technology that is routinely used in computational quantum chemistry, including in our relativistic molecular structure code, BERTHA. We demonstrate that, unlike the kinetically matched two-component basis sets that are widely employed in relativistic quantum chemistry, the CKG-spinor basis is able to reproduce the well-known eigenvalue spectrum of point-nuclear hydrogenic systems to high accuracy for all atomic symmetry types. Calculations are reported of third- and higher-order vacuum polarization effects in hydrogenic systems using the CKG-spinor set. These results reveal that Gaussian basis set expansions are able to calculate accurately these QED effects without recourse to the apparatus of regularization and in agreement with existing methods. An approach to the evaluation of the electron self-energy is outlined that extends our earlier work using partial-wave expansions in QED. Combined with the treatment of vacuum polarization effects described in this article, these basis set methods suggest the development of a comprehensive ab initio approach to the calculation of radiative and QED effects in future versions of the GRASP code. [ABSTRACT FROM AUTHOR]

We study the time-momentum representation of the kernel needed to compute the hadronic vacuum polarization contribution to the muon g -2 in the space-like region at next-to-leading order. For small values of the time, we present analytical series expansions; for large values of the time, we present numerical series expansions which overcome the problems showed by naïve asymptotic expansions. These results are to be employed in lattice QCD determination of the hadronic vacuum polarization contribution to the muon g -2 at next-to-leading order. [ABSTRACT FROM AUTHOR]