One-loop Vacuum Polarization Research Articles

The Average Radial Speed of Light From Near to Far Space Surrounding the Kerr–Newman Super-Gravitational Source

The Kerr–Newman metric is used to discuss the average radial speed of light from near to far space surrounding the super-gravitational source like a black hole which can be observed by a weak-gravitational reference frame such as an observer on the Earth. The velocity equation of light near the black hole is represented by the Boyer–Lindquist coordinates (t, r, θ, and ϕ), and the main parameters are the Schwarzschild radius RS, the rotation term a, and the charged term RQ. From the calculations, the average radial speed of light from r = RS to r = αRS with α>1 is possibly observed exceeding c by an observer on the Earth. The result can extend to the large r place when the rotation of the black hole is high or the charge is very large. This average radial speed finally approaches c far away from the black hole. We also propose a new explanation based on our results that the observation of the faster-than-light particle is due to the light bending near the Kerr–Newman black hole or supermassive star with very strong gravity. In addition, two superluminal theories used to explain the speed of light in astronomy are compared. One is the Doppler effect in special relativity, and the other is the change in the photon speed due to the QED contribution of one-loop vacuum polarization to the photon effective action. The former seems to mainly appear as the change of the observed wavelength or frequency, while the latter is probably the random and irregular occurrences. Our explanation is based on the Kerr–Newman metric in general relativity, and it extends the discussion from the flat spacetime in special relativity to the curved spacetime which is suitable for many superluminal observations near the super-gravitational sources like the black hole. Our calculations are used to verify tangible observations like the M87 jet.

Winding number dependence of quantum vortex energies at one-loop

We compute the one-loop vacuum polarization energies of Abrikosov-Nielsen-Olesen vortices with topological charge $n$ in scalar electrodynamics, for the Bogomolny-Prasad-Sommerfeld case of equal gauge and scalar masses. This calculation allows us to investigate the relationship between the winding number and the quantum-corrected vortex energy, which in turn determines the stability of higher winding configurations against decay into configurations with unit winding. While the classical energy is proportional to $n$, we find that the vacuum polarization energy is negative and approximately proportional to $n\ensuremath{-}1$ with a small constant offset.

Virtual Hawking Radiation.

We consider the effects of off shell Hawking radiation on scattering processes involving black holes coupled to quantum fields. The focus here is on the case of gravitational scattering of a scalar field mediated by the exchange of virtual Hawking gravitons from a four-dimensional Schwarzschild black hole. Our result is obtained in the context of a worldline effective field theory for the black hole and is valid in the semiclassical limit where the Schwarzschild radius r_{s} is larger than the Planck length 1/m_{Pl}. In addition, we assume that four-momentum exchange q is smaller than r_{s}^{-1} and that the incoming particle has energy larger then the black hole's Hawking temperature. The inelastic cross section we obtain is a new, leading-order quantum gravity effect, arising at the same order in q^{2}/m_{Pl}^{2} as the well-understood one-loop graviton vacuum polarization corrections to gravitational scattering between massive particles.

Vacuum polarization in Siklos spacetimes

We study the effect of one-loop vacuum polarization on photon propagation in Siklos spacetimes in the geometric optics limit. We show that for photons with a general polarization in the transverse plane, the quantum correction vanishes in spacetimes with $H_{xy}=0$. For photons polarized along a transverse axis, subluminal and superluminal solutions are admitted for certain subclasses of Siklos spacetimes. We investigate the results in the Kaigorodov and Defrise spacetimes and obtain explicit expressions for the phase velocities. In Kaigorodov spacetime with $H\sim x^3$, photons polarized along $x$-axis are subluminal in regions where $H$ is positive, and superluminal in regions where $H$ is negative, while photons polarized along $y$-axis are superluminal in $H>0$ regions and subluminal in $H<0$ regions. In Defrise spacetime, $H\sim x^{-2}$, $x$-polarized and $y$-polarized photons are superluminal for $H<0$ and subluminal for $H>0$. We comment on motion in other Siklos spacetimes.

One-loop vacuum polarization at mα7 and higher orders for three-body molecular systems

We present calculations of the one-loop vacuum polarization correction (Uehling potential) for the three-body problem in the NRQED formalism. The case of one-electron molecular systems is considered. Numerical results of the vacuum polarization contribution at m$\alpha$7 and higher orders for the fundamental transitions (v = 0, L = 0) $\rightarrow$ (v ' = 1, L ' = 0) in the H2+ and HD+ molecular ions are presented and compared with calculations performed in the adiabatic approximation. The residual uncertainty from this contribution on the transition frequencies is shown to be of a few tens of Hz.

Hyperfine structure of S-states of muonic tritium

On the basis of quasipotential method in quantum electrodynamics we carry out a precise calculation of hyperfine splitting of S-states in muonic tritium. The one-loop and two-loop vacuum polarization corrections, relativistic effects, nuclear structure corrections in first and second orders of perturbation theory are taken into account. The contributions to hyperfine structure are obtained in integral form and calculated analytically and numerically. Obtained results for hyperfine splitting can be used for a comparison with future experimental data of CREMA collaboration.

One-Loop Contribution to the Matter-Driven Expansion of the Universe

Standard perturbative quantum gravity formalism is applied to compute the lowest order corrections to the spatially flat cosmological FLRW solution governed by ordinary matter. The presented approach is analogous to the one used to compute quantum corrections to the Coulomb potential in electrodynamics, or to the approach applied in computation of quantum corrections to the Schwarzschild solution in gravity. In this framework, it is shown that the corrections to the classical metric coming from the one-loop graviton vacuum polarization (self-energy) have (UV cutoff dependent) repulsive properties, which could be not negligible in the very early Universe.

Ground state hyperfine structure in muonic lithium ions

On the basis of perturbation theory in the fine structure constant α and the mass ratio of the electron and muon, we calculate the one-loop vacuum polarization, electron vertex corrections, nuclear structure and recoil corrections of the hyperfine splitting of the ground state in muonic lithium ions and . We obtain complete results for small hyperfine splittings of the ground state in of MHz and MHz and in MHz and MHz, which can be regarded as a reliable estimates for comparison with future experimental data.

Bound-state QED calculations for antiprotonic helium

We present new theoretical results for the transition energies of the hydrogen isotope molecular ions and antiprotonic helium atoms. Our consideration includes corrections at the mα 7 order in the nonrecoil limit such as the one-loop self-energy, one-loop vacuum polarization, Wichman-Kroll, and complete two-loop contributions. That allowed to get transition energies for the fundamental transition \((v = 0,L = 0)\rightarrow (1,0)\) in the hydrogen molecular ion with the relative theoretical uncertainty of ∼7⋅10−12 that corresponds to a fractional precision of 1.5⋅10−11 in determination of the electron-to-proton mass ratio, m p /m e . Correspondingly, for the two-photon transitions in the antiprotonic helium we have 4.7⋅10−11 as a relative uncertainty for the \((33,32)\rightarrow (31,30)\) transition frequency and a fractional precision of 3.6⋅10−11 for an inferred antiproton-to-electron mass ratio.

One-loop vacuum polarization atmα7order for the two-center problem

We present calculations of the one-loop vacuum polarization contribution (Uehling potential) for the two-center problem in the NRQED formalism. The cases of hydrogen molecular ions ($Z_1=Z_2=1$) as well as antiprotonic helium ($Z_1=2$, $Z_2=-1$) are considered. Numerical results of the vacuum polarization contribution at $m\alpha^7$ order for the fundamental transitions $(v=0,L=0)\to(v'=1,L'=0)$ in H$_2^+$ and HD$^+$ are presented.

The Epstein–Glaser causal approach to the light-front QED4. II: Vacuum polarization tensor

In this work we show how to construct the one-loop vacuum polarization for light-front QED4 in the framework of the perturbative causal theory. Usually, in the canonical approach, it is considered for the fermionic propagator the so-called instantaneous term, but it is known in the literature that this term is controversial because it can be omitted by computational reasons; for instance, by compensation or vanishing by dimensional regularization. In this work we propose a solution to this paradox. First, in the Epstein–Glaser causal theory, it is shown that the fermionic propagator does not have instantaneous term, and with this propagator we calculate the one-loop vacuum polarization, from this calculation it follows the same result as those obtained by the standard approach, but without reclaiming any extra assumptions. Moreover, since the perturbative causal theory is defined in the distributional framework, we can also show the reason behind our obtaining the same result whether we consider or not the instantaneous fermionic propagator term.

Relativistic recoil effects for energy levels in a muonic atom within a Grotch-type approach. II. An application to the one-loop electronic vacuum polarization

We continue our account of relativistic recoil effects in muonic atoms and present explicitly analytic results at first order in electron-vacuum-polarization effects. The results are obtained within a Grotch-type approach based on an effective Dirac equation. Some expressions are cumbersome and we investigate their asymptotic behavior. Previously relativistic two-body effects due to the one-loop electron vacuum polarization were studied by several groups. Our results found here are consistent with the previous result derived within a Breit-type approach (including ours) and disagree with a recent attempt to apply a Grotch-type approach.

Covariant vacuum polarizations on de Sitter background

We derive covariant expressions for the one-loop vacuum polarization induced by a charged scalar on de Sitter background. Two forms are employed: one in which two covariant derivatives act on de Sitter-invariant basis tensors multiplied by scalar structure functions, and the other in which four covariant derivatives act on a single basis tensor times a structure function. The second representation permits the correction to dynamical photons to be expressed as a surface integral, which raises the important question of what sorts of effects can be absorbed into corrections of the initial state. Results are obtained for charged, minimally coupled scalars which are either massless or else light. The former show de Sitter breaking whereas the latter are de Sitter invariant. However, the de Sitter-invariant formulation does not seem useful, even when it is possible. Our work has two important physical consequences: (1) an upcoming computation of the vacuum polarization from inflationary gravitons should be expressed using the old, noncovariant formalism, and (2) one should re-examine the conclusion of a previous study of the effect of inflationary scalars on gravitons.

One-Loop Quantum Gravity Repulsion in the Early Universe

Perturbative quantum gravity formalism is applied to compute the lowest order corrections to the classical spatially flat cosmological Friedmann-Lemaître-Robertson-Walker solution (for the radiation). The presented approach is analogous to the approach applied to compute quantum corrections to the Coulomb potential in electrodynamics, or rather to the approach applied to compute quantum corrections to the Schwarzschild solution in gravity. In the framework of the standard perturbative quantum gravity, it is shown that the corrections to the classical deceleration, coming from the one-loop graviton vacuum polarization (self-energy), have (UV cutoff free) opposite to the classical repulsive properties which are not negligible in the very early Universe. The repulsive "quantum forces" resemble those known from loop quantum cosmology.

Nuclear-size correction to the Lamb shift of one-electron atoms

The nuclear-size effect on the one-loop self-energy and vacuum polarization is evaluated for the $1s$, $2s$, $3s$, $2{p}_{1/2}$, and $2{p}_{3/2}$ states of hydrogen-like ions. The calculation is performed to all orders in the nuclear binding strength parameter $Z\ensuremath{\alpha}$. Detailed comparison is made with previous all-order calculations and calculations based on the expansion in the parameter $Z\ensuremath{\alpha}$. Extrapolation of the all-order numerical results obtained toward $Z=1$ provides results for the radiative nuclear-size effect on the hydrogen Lamb shift.

Vacuum polarization from confined fermions in3+1dimensions

We study the main properties of the one-loop vacuum polarization function for massless spinor QED4 in a slab, namely, with fields defined on M in R^(3+1), such that M = {(x0, ..., x3)|0 <= x3 <= epsilon}, and bag-like boundary conditions on the boundary. We evaluate the induced charge density and current due to an external constant electric field normal to the boundary; we also study the effective action for a purely transverse field, identifying its epsilon-dependent contribution.

Large scale magnetic fields from gravitationally coupled electrodynamics

The generation of primordial magnetic seed fields during inflation is studied in a theory derived from the one-loop vacuum polarization effective action of the photon in a curved background. This includes terms which couple the curvature to the Maxwell tensor. The resulting magnetic field strength is estimated in a model where the inflationary phase is directly matched to the standard radiation dominated era. The allowed parameter region is analyzed and compared with the bounds necessary to seed the galactic magnetic field. It is found that magnetic fields of cosmologically interesting field strengths can be generated.

Two-Component Description for Relativistic Fermions

We propose a two-component form to describe massive relativistic fermions in gauge theories. Relations between the Green's functions in this form and those in the conventional four-component form are derived. It is shown that the S-matrix elements in both forms are exactly the same. The description of the fermion in the new form simplifies significantly the γ-matrix algebra in the four-component form. In particular, in perturbative calculations the propagator of the fermion is a scalar function. As examples, we use this form to reproduce the relativistic spectrum of hydrodron atom, the S-matrix of e+e− → μ+ μ− and QED one-loop vacuum polarization of photon.

Binding two-loop vacuum-polarization corrections to the bound-electrongfactor

We commence the evaluation of the one- and two-loop binding corrections to the $g$ factor for an electron in a hydrogenlike system of order ${\ensuremath{\alpha}}^{2}{(Z\ensuremath{\alpha})}^{5}$ and consider diagrams with closed fermion loops. The one-loop vacuum-polarization correction is rederived and confirmed. For the two-loop vacuum-polarization correction, due to a specific gauge-invariant set of diagrams with closed fermion loops, we find a correction $\ensuremath{\delta}g=7.442{(\ensuremath{\alpha}/\ensuremath{\pi})}^{2}{(Z\ensuremath{\alpha})}^{5}$. Based on the numerical trend of the coefficients inferred from the gauge-invariant subset, we obtain a numerically large tentative estimate for the complete two-loop binding correction to the $g$ factor (sum of self-energy and vacuum polarization).

Electromagnetic and Scalar Pion form factor in the Kroll-Lee-Zumino model

The renormalizable Abelian quantum field theory model of Kroll, Lee, and Zumino is used at the one loop level to compute vertex corrections to the tree-level, Vector Meson Dominance (VMD) electromagnetic pion form factor. These corrections, together with the one-loop vacuum polarization contribution, imply a resulting electromagnetic pion form factor in excellent agreement with data in the whole range of accessible momentum transfers in the space-like region. The time-like form factor, which reproduces the Gounaris-Sakurai formula at and near the rho-meson peak, is unaffected by the vertex correction at order $\cal{O}$$(g^2)$. The KLZ model is also used to compute the scalar radius of the pion at the one loop level, finding $<r^{2}_{\pi}>_{S} = 0.40 fm^{2}$. This value implies for the low energy constant of chiral perturbation theory $\bar{l}_{4} =3.4$.