Charge Renormalization Research Articles

Time-dependent charge renormalization procedure in QED

We examine the formation process of the vacuum polarization cloud around a localized charge with space-time resolution permitting us to view the traditional charge renormalization procedure from a dynamical perspective. The asymptotic steady-state charge cloud found in the long-time limit (after the subtraction of a suitable term) matches the distribution predicted by standard perturbative propagator techniques based on Feynman diagrams. This match demonstrates that an alternative (classical-field approximation based) approach can predict the nonlinear properties of the vacuum state. It turns out that some aspects of the polarization dynamics suggest that the vacuum can be viewed as a classical dielectric medium, while other aspects are purely quantum mechanical in nature and cannot be predicted from the Maxwell theory for classical fields.

Collapse of electrons to a donor cluster inSrTiO3

It is known that a nucleus with charge $Ze$ where $Z>170$ creates electron-positron pairs from the vacuum. These electrons collapse onto the nucleus resulting in a net charge $Z_n<Z$ while the positrons are emitted. This effect is due to the relativistic dispersion law. The same reason leads to the collapse of electrons to the charged impurity with a large charge number $Z$ in narrow-band gap semiconductors and Weyl semimetals as well as graphene. In this paper, a similar effect of electron collapse and charge renormalization is found for donor clusters in SrTiO$_3$ (STO), but with a very different origin. At low temperatures, STO has an enormously large dielectric constant. Because of this, the nonlinear dielectric response becomes dominant when the electric field is not too small. We show that this leads to the collapse of surrounding electrons into a charged spherical donor cluster with radius $R$ when its total charge number $Z$ exceeds a critical value $Z_c\simeq R/a$ where $a$ is the lattice constant. Using the Thomas-Fermi approach, we find that the net charge $Z_ne$ grows with $Z$ until $Z$ exceeds another value $Z^*\simeq(R/a)^{9/7}$. After this point, $Z_n$ remains $\sim Z^*$. We extend our results to the case of long cylindrical clusters. Our predictions can be tested by creating discs and stripes of charge on the STO surface.

Plasmon signature in Dirac-Weyl liquids

We consider theoretically as a function of temperature the plasmon mode arising in three-dimensional Dirac liquids, i.e., systems with linear chiral relativistic single-particle dispersion, within the random phase approximation. We find that whereas no plasmon mode exists in the intrinsic (undoped) system at zero temperature, there is a well-defined finite-temperature plasmon with superlinear temperature dependence, rendering the plasmon dispersion widely tunable with temperature. The plasmon dispersion contains a logarithmic correction due to the ultraviolet-logarithmic renormalization of the electron charge, manifesting a fundamental many-body interaction effect as in quantum electrodynamics. The plasmon dispersion of the extrinsic (doped) system displays a minimum at finite temperature before it crosses over to the superlinear intrinsic behavior at higher temperature, implying that the high-temperature plasmon is a universal feature of Dirac liquids irrespective of doping. This striking characteristic temperature dependence of intrinsic Dirac plasmons along with the logarithmic renormalization is a unique manifestation of the three-dimensional relativistic Dirac nature of quasiparticle excitations and serves as an experimentally observable signature of three-dimensional Dirac materials.

Charge Renormalization for Ellipsoidal Macroions.

We study the problem of counterion condensation for ellipsoidal macroions, a geometry well-suited for modeling liquid crystals, anisotropic vesicles, and polymers. We find that the ions within an ellipsoid's condensation layer are relatively unrestricted in their motions, and consequently work to establish a quasi-equipotential at its surface. This simplifies the application of Alexander et al.'s procedure, enabling us to obtain accurate analytic estimates for the critical valence of a general ellipsoid in the weak screening limit. Interestingly, we find that the critical valence of an eccentric ellipsoid is always larger than that of the sphere of equal volume, implying that counterion condensation provides a force resisting the deformation of spherical macroions. This contrasts with a recent study of flexible spherical macroions, which observed a preference for deformation into flattened shapes when considering only linear effects. Our work suggests that the balance of these competing forces might alter the nature of the transition.

Interaction of static charges in graphene

The study of the interaction potential between static charges within Monte-Carlo simulation of graphene is carried out. The numerical simulations are performed in the effective lattice field theory with noncompact 3 + 1-dimensional Abelian lattice gauge fields and 2 + 1-dimensional staggered lattice fermions. At low temperature the interaction can be described by the Coulomb potential reduced by some dielectric permittivity ϵR. The dependence of ϵR on the dielectric permittivity of substrate is determined. In addition, the renormalization of the quasiparticle charge is studied. At large temperatures the interaction potential can be described by the two-dimensional Debye screening. The dependence of Debye screening mass on the dielectric permittivity of substrate allows to determine the position of the insulator-semimetal phase transition. It is shown that graphene reveals in the semimetal phase the properties of the two-dimensional plasma of fermions excitations.

Equilibrium properties of charged microgels: A Poisson-Boltzmann-Flory approach

The equilibrium properties of ionic microgels are investigated using a combination of the Poisson-Boltzmann and Flory theories. Swelling behavior, density profiles, and effective charges are all calculated in a self-consistent way. Special attention is given to the effects of salinity on these quantities. In accordance with the traditional ideal Donnan equilibrium theory, it is found that the equilibrium microgel size is strongly influenced by the amount of added salt. Increasing the salt concentration leads to a considerable reduction of the microgel volume, which therefore releases its internal material - solvent molecules and dissociated ions - into the solution. Finally, the question of charge renormalization of ionic microgels in the context of the cell model is briefly addressed.

Coordinate-space approach to vacuum polarization

The vacuum-polarization correction for bound electrons or muons is examined. The objective is to formulate a framework for calculating the correction from bound-state quantum electrodynamics entirely in coordinate space, including the Uehling potential which is usually isolated and treated separately. Pauli-Villars regularization is applied to the coordinate-space calculation and the most singular terms are shown to be eliminated, leaving the physical correction after charge renormalization. The conventional derivation of the Uehling potential in momentum space is reviewed and compared to the coordinate-space derivation.

Running couplings in quantum theory of gravity coupled with gauge fields

In this paper we study the coupled system of non-abelian gauge fields with higher-derivative gravity. Charge renormalization is investigated in this coupled system. It is found that the leading term in the gauge coupling beta function comes due to interaction of gauge fields with gravitons. This is shown to be a universal quantity in the sense that it doesn't depend on the gauge coupling and the gauge group, but may depend on the other couplings of the action (gravitational and matter). The coupled system is studied at one-loop. It is found that the leading term of gauge beta function is zero at one-loop in four dimensions. The effect of gauge fields on the running of gravitational couplings is investigated. The coupled system of gauge field with higher-derivative gravity is shown to satisfy unitarity when quantum corrections are taken in to account. Moreover, it is found that Newton constant goes to zero at short distances. In this renormalizable and unitary theory of gauge field coupled with higher-derivative gravity, the leading term of the gauge beta function, found to be universal for all gauge groups, is further studied in more detail by isolating it in the context of abelian gauge theories coupled with gravity in four dimensions. Using self-duality of abelian gauge theories in four dimensions, this term of the gauge beta function is shown to be zero to all loops. This is found to be independent of the gravity action, regularization scheme and gauge fixing condition. An explicit one-loop computation for arbitrary gravity action further demonstrates the vanishing of this term in the gauge beta function in four dimensions, independent of the regularization scheme and gauge fixing condition. Consequences of this are discussed.

Three-loop calculations in non-abelian gauge theories

A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous dimensions for non-Abelian gauge theories with fermions in the three-loop approximation. A three-loop expression for the effective charge of QCD is given. Charge renormalization effects in the SU(4)-supersymmetric gauge model is shown to vanish at this level. A complete list of required formulas is given in Appendix. The above-mentioned results of three-loop calculations were published by the present authors (with A.Yu. Zharkov and L.V. Avdeev) in 1980 in Physics Letters B. The present text, which treats the subject in more details and contains a lot of calculational techniques, was also published in 1980 as the JINR Communication E2-80-483.

Charge renormalization due to graviton loops

The leading term in the gauge coupling beta function comes due to interaction of gauge field with gravitons. It is shown to be a universal quantity for all gauge theories. At one-loop it is found to be zero in four dimensions. This is independent of the gravity action with metric as the field variable, gauge fixing condition and regularization scheme. This term being universally same for all gauge groups is further studied in the case of abelian gauge theories, where due to self-duality this term is shown to be zero to all loops, on-shell. Consequences of this are discussed.

Magnetic field-induced gluonic (inverse) catalysis and pressure (an)isotropy in QCD

We study the influence of strong external magnetic fields on gluonic and fermionic observables in the QCD vacuum at zero and nonzero temperatures, via lattice simulations with N_f=1+1+1 staggered quarks of physical masses. The gluonic action density is found to undergo magnetic catalysis at low temperatures and inverse magnetic catalysis near and above the transition temperature, similar to the quark condensate. Moreover, the gluonic action develops an anisotropy: the chromo-magnetic field parallel to the external field is enhanced, while the chromo-electric field in this direction is suppressed. We demonstrate that the same hierarchy is obtained using the Euler-Heisenberg effective action. Conversely, the topological charge density correlator does not reveal a significant anisotropy up to magnetic fields eB~1 GeV^2. Furthermore, we show that the pressure remains isotropic even for nonzero magnetic fields, if it is defined through a compression of the system at fixed external field. In contrast, if the flux of the field is kept fixed during the compression -- which is the situation realized in the lattice simulation -- the pressure develops an anisotropy. We estimate the quark and gluonic contributions to this anisotropy, and relate them to the magnetization of the QCD vacuum. After performing electric charge renormalization, we obtain an estimate for the magnetization, which indicates that QCD is paramagnetic.

Renormalization of the cyclic Wilson loop

In finite-temperature field theory, the cyclic Wilson loop is defined as a rectangular Wilson loop spanning the whole compactified time direction. In a generic non-abelian gauge theory, we calculate the perturbative expansion of the cyclic Wilson loop up to order g^4. At this order and after charge renormalization, the cyclic Wilson loop is known to be ultraviolet divergent. We show that the divergence is not associated with cusps in the contour but is instead due to the contour intersecting itself because of the periodic boundary conditions. One consequence of this is that the cyclic Wilson loop mixes under renormalization with the correlator of two Polyakov loops. The resulting renormalization equation is tested up to order g^6 and used to resum the leading logarithms associated with the intersection divergence. Implications for lattice studies of this operator, which may be relevant for the phenomenology of quarkonium at finite temperature, are discussed.

Charge Renormalization and Static Electron/Positron Pair Production for a Nonlinear Dirac Model with Weak Interactions

The Hartree--Fock approximation of quantum electrodynamics provides a rigorous framework for the description of relativistic electrons in external fields. This nonlinear model takes into account the infinitely many virtual electrons of Dirac's vacuum as well as the Coulomb interactions between all the particles. The state of the system is an infinite-rank projection satisfying a nonlinear equation. In this paper, we construct solutions to this equation in the regime of weak interactions (that is, small coupling constant $\alpha$) and strong external fields (that is, large atomic charge $Z$ such that $\alpha Z:=\kappa$ stays fixed). In this regime, we are able to remove the ultraviolet cutoff $\Lambda$ as soon as $\alpha\log\Lambda$ stays fixed. As an application of this result, we compare the critical strength $\kappa_c(\alpha)$ of the external potential needed to produce an additional particle in the vacuum, when $\alpha=0$ or $\alpha>0$. We prove that $\lim_{\alpha\to 0}\kappa_c(\alpha)/\kappa_c(0)> 1$, and we identify the limit exactly. Because of the dielectric behavior of Dirac's vacuum, static electron/positron pair production occurs in the interacting case for a stronger field than in the noninteracting case, which is a mere consequence of charge renormalization.

Spherically symmetric Einstein–Maxwell theory and loop quantum gravity corrections

Effects of inverse triad corrections and (point) holonomy corrections, occurring in loop quantum gravity, are considered on the properties of Reissner–Nordström black holes. The version of inverse triad corrections with unmodified constraint algebra reveals the possibility of occurrence of three horizons (over a finite range of mass) and also shows a mass threshold beyond which the inner horizon disappears. For the version with modified constraint algebra, coordinate transformations are no longer a good symmetry. The covariance property of spacetime is regained by using a quantum notion of mapping from phase space to spacetime. The resulting quantum effects in both versions of these corrections can be associated with renormalization of either mass, charge or wavefunction. In neither of the versions, Newton’s constant is renormalized. (Point) Holonomy corrections are shown to preclude the undeformed version of constraint algebra as also a static solution, though time-independent solutions exist. A possible reason for difficulty in constructing a covariant metric for these corrections is highlighted. Furthermore, the deformed algebra with holonomy corrections is shown to imply signature change.

Charge renormalization of bilayer elastic properties

By combining molecular dynamics simulations and analytical arguments, we investigate the elastic properties of charged lipid bilayers. We show that electrostatic interactions between the head groups can lead to solidification of the lipid bilayer that would otherwise be in a liquid state if the charges were absent. All elastic parameters of the bilayer such as the bending rigidity κ and the two-dimensional bulk modulus λ and Young's modulus Y are found to depend on the values of the charges assigned to the lipid head groups. To extract κ and λ, we fit the molecular dynamics data to a standard elastic model for lipid bilayers. Moreover, we analytically obtain the dependence of the Young modulus Y on the relative strengths of electrostatic and van der Waals interactions in the zero temperature limit.

Frequency domain photon migration measurements of dense monodisperse charged lattices and analysis using solutions of Ornstein Zernike equations

Isotropic scattering coefficient measurements were made of monodisperse polystyrene lattices of two different diameters of 144nm and 223nm and at volume fractions ranging from 0.15 to 0.22, using frequency domain photon migration measurements at wavelengths of 660, 685, 785 and 828nm. The isotropic scattering coefficient measurements were shown to be sensitive to the changing ionic strength (0.5–4mM, NaCl equiv.) of the dispersions exhibiting hindered scattering owing to structure at the lowest ionic strength values. Monte Carlo simulations and numerical solution of the Ornstein Zernike equations were used to compute isotropic scattering coefficients for comparison to measured values. The interaction potential was modeled as a hard sphere Yukawa potential and the Hypernetted Chain closure was used to solve the OZ equation. Effective particle charges were found after renormalization of the bare particle charge and used to predict the isotropic scattering coefficient. The model data were found to follow similar trends as experimental measurements. The refractive index of the particles has found to be an important factor for predicting experimental isotropic scattering coefficient values.

Charge independence, charge symmetry breaking in theS-wave nucleon-nucleon interaction, and renormalization

We study the interplay between charge symmetry breaking and renormalization in the NN system for s-waves. We find a set of universality relations which disentangle explicitly the known long distance dynamics from low energy parameters and extend them to the Coulomb case. We analyze within such an approach the One-Boson-Exchange potential and the theoretical conditions which allow to relate the proton-neutron, proton-proton and neutron-neutron scattering observables without the introduction of extra new parameters and providing good phenomenological success.

Toms replies

Replying to J. Ellis & N. E. Mavromatos , doi:10.1038/nature10619 (2011) In a previous paper1, I used the gauge-invariant background-field method to calculate a contribution to the renormalization of electric charge due to quantum gravity that was quadratically dependent on an energy cut-off. This was done by taking a constant electromagnetic background field, F. The result was used to support the original suggestion of Robinson and Wilczek2 that quadratic divergences could lead to asymptotic freedom. This result has been criticized by Ellis and Mavromatos3 and their present submission4 gives a shortened and altered discussion of their viewpoint.

Renormalization and Asymptotic Expansion of Dirac’s Polarized Vacuum

We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization effects. We consider the total physical density ρ ph including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no ‘real’ electron. We show that ρ ph admits an asymptotic expansion to any order in powers of the physical coupling constant α ph, provided that the ultraviolet cut-off behaves as \({\Lambda\sim e^{3\pi(1-Z_3)/2\alpha_{\rm ph}} \gg 1}\). The renormalization parameter 0 < Z 3 < 1 is defined by Z 3 = α ph/α, where α is the bare coupling constant. The coefficients of the expansion of ρ ph are independent of Z 3, as expected. The first order term gives rise to the well-known Uehling potential, whereas the higher order terms satisfy an explicit recursion relation.

Dielectric Relaxations of Ionic Thiol-Coated Noble Metal Nanoparticles in Aqueous Solutions: Electrical Characterization of the Interface

The radiowave dielectric properties of organothiol monolayer-protected Au and Ag metallic nanoparticles have been investigated in the frequency range of 10 kHz to 2 GHz, where a dielectric relaxation, due to the polarization of the ionic atmosphere at the aqueous interface, occurs. The simultaneous measurement of the particle size, by means of dynamic light scattering technique, and of the particle electrical charge, by means of laser microelectrophoresis technique, allow us to describe the whole dielectric behavior at the light of the standard electrokinetic model for charged colloidal particles. Au and Ag metallic nanoparticles experience a large charge renormalization, in agreement with the counterion condensation effect for charged spherical colloidal particles. The value of the effective valence Z(eff) of each nanoparticle investigated has been evaluated thanks to the dielectric parameters of the observed relaxation process and further confirmed by direct current electrical conductivity measurements. All in all, these results provide support for the characterization of the electrical interfacial properties of metallic nanoparticles by means of dielectric relaxation measurements.