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Gravitational field of cosmic strings in theories with extra spatial dimensions differs significantly from that in the 4D Einstein's theory. This means that all gravity induced properties of cosmic strings need to be revised. Here we consider the effect of vacuum polarization outside a straight infinitely thin cosmic string embedded in RS2 brane world.

The collective multipole excitations are studied in the framework of relativistic random-phase approximation with the vacuum polarization. First, we show for the nuclear ground state that the leading order of derivative expansion of the effective action arising from the vacuum correction agrees with the exact calculation using the Green function method very well. The derivative expansion makes us easy to perform a fully self-consistent calculation, even for the random-phase approximation. A remarkable effect of the inclusion of the vacuum polarization is the increase of the effective mass m_eff/m_N ~ 0.9, which gives, for all multipole modes, smaller energy-weighted sum rule values than those of the typical relativistic model. Also, the large effective mass constrained by the vacuum polarization can give an excellent agreement with experimental data on the excitation energy for the isoscalar quadrupole resonances. It is shown, further, that the change of the shell structure due to the vacuum polarization plays an important role in the dipole compression modes.

We analyze wave propagation in the vacuum of Podolsky regularized electrodynamics. Two kinds of waves were found in the theory: the traditional non-dispersive waves of Maxwell electrodynamics, and a dispersive wave reminiscent of wave propagation in a collisionless plasma. Charged particle concentration was determined, and found to be huge in this vacuum. We interpret the results in terms of vacuum polarization effects induced in an otherwise classical theory.

In this paper, we use Krein regularization to study certain standard computations in quantum chromodynamics (QCD). In this method, the auxiliary modes— those with negative norms— are employed to calculate the quark self-energy, vacuum polarizations and vertex functions. We explicitly show that after making use of these modes and by taking into account the quantum metric fluctuation for the problems at hand, the conventional results can indeed be reproduced; but with the advantage of finite answers which require fewer mathematical procedures. An obvious merit of this approach is that the theory is naturally renormalized. The ultraviolet (UV) divergences disappear due to the presence of negative norm state, similar to the Pauli–Villars regularization method. We compare the answers of Krein regularization with the results of calculations which have been done in Hilbert space.

Vacuum polarization of charged massless fermions is investigated in the superposition of Coulomb and Aharonov–Bohm (AB) potentials in 2 + 1 dimensions. For this purpose, we construct the Green function of the two-dimensional Dirac equation with Coulomb and AB potentials (via the regular and irregular solutions of the radial Dirac equation) and then calculate the vacuum polarization charge density in the so-called subcritical and supercritical regimes. In the supercritical regime, the Green function has a discontinuity in the complex plane of “energy” due to the singularities on the negative energy axis; these singularities are situated on the unphysical sheet and related to the creation of infinitely many quasistationary fermionic states with negative energies. We expect that our results will be helpful in gaining deeper understanding of the fundamental problem of quantum electrodynamics which can be applied to the problems of charged impurity screening in graphene taking into consideration the electron spin.

We want to study the influence of the quantum vacuum on light propagation. At first, by working in the standard linear quantum theory of the electromagnetic fields, it is shown that the electric permittivity and the magnetic permeability of the vacuum medium are changed; but, the resulting speed of light is not modified. Then, taking into account nonlinear effects by considering the Euler–Heisenberg Lagrangian, the corresponding zero point (vacuum) energy and the resulting modification of the speed of light are found up to the first nonvanishing correction.

In this paper, one of the most important diagrams of weak interaction (vacuum polarization) is studied in Krein space quantization (KSQ). This diagram has divergent terms in Hilbert space which must be eliminated using a traditional regularization method like dimensional regularization whereas in KSQ the result is automatically finite and does not need renormalization.

In this paper we compute the correction to the entropy of Schwarzschild black hole due to the vacuum polarization effect of massive scalar field. The Schwarzschild black hole is supposed to be confined in spherical shell. The scalar field obeying mixed boundary condition on the spherical shell.

In this paper we investigate vacuum polarization effects associated with charged massive quantum fermionic fields in a six-dimensional cosmic string space-times considering the presence of a magnetic flux running along its core. We have shown that for specific values of the parameters which codify the presence of the cosmic string, and the fractional part of the ratio of the magnetic flux by the quantum one, a closed expression for the respective Green function is obtained. Adopting this result, we explicitly calculate the renormalized vacuum expectation value of the energy-momentum tensor, , and analyse this result in some limiting cases.

We discuss consistency of the concept of external background in QFT. Different restrictions on magnitude of magnetic and electric fields are analyzed. The back reaction due to strong electric field is calculated and restrictions on the magnitude and duration of such a field are obtained. The problem of consistency of Dirac equation with a superstrong Coulomb field is discussed.

We consider the effect of the magnetic field background in the form of a tube of the finite transverse size on the vacuum of the quantized charged massive scalar field which is subject to the Dirichlet boundary condition at the edge of the tube. The vacuum energy is induced, being periodic in the value of the magnetic flux enclosed in the tube. The dependence of the vacuum energy density on the distance from the tube and on the coupling to the space-time curvature scalar is comprehensively analyzed.

In this paper we compute and study the Casimir energy, vacuum polarization and the resulting fermion fractionalization, the phase shifts and the stability of the bound states of a Dirac field, all due to its interaction with an electric potential in (1+1) dimension. We also explore the inter-relation between these effects. All of these effects are different manifestations of one single source, which is the distortion of the fermionic spectrum and appears as spectral deficiencies in the continua and bound states. We compute and display the spatial densities of these deficiencies and those of the bound states, along with their associated energy densities. We find that in both cases the total spatial densities of states with E > 0 and E < 0 are exact mirror images of each other. Therefore these densities for the complete spectrum are unchanged as compared to the free case, and in particular they remain uniform. The densities of states with E < 0 are precisely the vacuum polarization density and the Casimir energy density, respectively. We find that the vacuum polarization is in general noninteger. We then compute and display the energy densities of the spectral deficiencies in the momentum space, and show that levels exiting or entering the continua leave their distinctive marks on these energy densities. We also use the phase shifts to calculate the Casimir energy and obtain the same result as in the direct calculation. In this problem the Casimir energy is always positive and is on the average an increasing function of the depth and width of the potential. It has a cusp whenever an energy level crosses E = 0. These cusps are local maxima in the extreme relativistic limits. Finally we show that the taking the Casimir energy into account, the total energy will be stable under small fluctuations in the parameters of the potential. However only the first two bound states are absolutely stable in the sense that their total energy is smaller than the mass.

Hattori–Itakura have recently derived the full Landau-level summation form for the photon vacuum polarization tensor in constant external magnetic fields at the one-loop level. The Landau-level summation form is essential when the photon momentum exceeds the threshold of the pair creation of charged particles in a magnetic field stronger than the squared mass of the charged particle. The tensor has three different form factors depending on the tensor direction with respect to the external magnetic field. The renormalization is nontrivial because these form factors are expressed in terms of double or triple summation forms. We give a numerical UV subtraction method which can be applied to numerically evaluate the form factors in constant external magnetic fields. We numerically investigate the photon vacuum polarization tensor in the form of the Landau-level summation and estimate the systematic errors coming from truncation of the Landau-level summation in a parameter region realized in heavy ion collision experiments. We find that the error is practically controllable at an O(10^-2) level for electrons and muons in strong magnetic fields expected in heavy ion collisions in the experimentally feasible kinematic parameter regions.

A perfectly reflecting (Dirichlet) boundary condition at the edge of an impenetrable magnetic-flux-carrying tube of nonzero transverse size is imposed on the charged massive scalar matter field which is quantized outside the tube. We show that the vacuum polarization effects outside the tube give rise to a macroscopic force acting at the increase of the tube radius (if the magnetic flux is held steady). The Casimir energy and force are periodic in the value of the magnetic flux, being independent of the coupling to the space–time curvature scalar. We conclude that a topological defect of the vortex type can polarize the vacuum of only those quantum fields that have masses which are much less than a scale of the spontaneous symmetry breaking.

The self-energy of photons at finite temperature is presented, up to the two-loop corrections, using the real-time formalism. The renormalized coupling constant has been derived in a form that is relevant for all the temperature ranges of interest in QED, specifically for the temperatures around $T\sim m$, where $m$ is the electron mass. Finite temperature modification mainly comes through the hot fermions when $T\ge m$. We use the calculations for the vacuum polarization to determine the dynamically generated mass of the photon, Debye screening length, and plasma frequency up to order ${\alpha }^2$ as well as the electromagnetic properties of the background medium in the temperature range $m\le T\le 2m$. At higher temperatures, the existing renormalization scheme does not work well because of the increase in the coupling constant. To exactly determine the validity of the renormalization scheme, the higher order calculations are required. The temperature, $T\sim m$, is of specific interest from the point of view of the early universe. Such calculations have also recently acquired significance due to the possibility of producing electron–positron plasma in the laboratory.

Here we analyze the finite temperature expectation values of the charge and current densities for a massive fermionic quantum field with nonzero chemical potential $\mu$, induced by a magnetic flux running along the axis of an idealized cosmic string. These densities are decomposed into the vacuum expectation values and contributions coming from the particles and antiparticles. Specifically the charge density is an even periodic function of the magnetic flux with the period equal to the quantum flux and an odd function of the chemical potential. The only nonzero component of the current density corresponds to the azimuthal current and it is an odd periodic function of the magnetic flux and an even function of the chemical potential. Both analyzed are developed for the cases where $\left|\mu \right|$ is smaller than the mass of the field quanta $m$.

A topological defect in the form of the Abrikosov–Nielsen–Olesen vortex is considered as a gauge-flux-carrying tube that is impenetrable for quantum matter. Charged scalar matter field is quantized in the vortex background with the perfectly reflecting (Dirichlet) boundary condition imposed at the side surface of the vortex. We show that a current circulating around the vortex and a magnetic field directed along the vortex are induced in the vacuum, if the Compton wavelength of the matter field exceeds considerably the transverse size of the vortex. The vacuum current and magnetic field are periodic in the value of the gauge flux of the vortex, providing a quantum-field-theoretical manifestation of the Aharonov–Bohm effect. The total flux of the induced vacuum magnetic field attains notable finite values even for the Compton wavelength of the matter field exceeding the transverse size of the vortex by just three orders of magnitude.

Nonperturbative vacuum polarization effects are explored for a supercritical Coulomb source with $Z>Z_{\mathrm{\text{cr}}}$ in 1+1D. Both the vacuum charge density ${\rho }_{\mathrm{\text{vac}}}(x)$ and vacuum energy $E_{\mathrm{\text{vac}}}$ are considered. It is shown that in the overcritical region the behavior of vacuum energy could be significantly different from perturbative quadratic growth up to decrease reaching large negative values.

Based on the original combination of analytical methods, computer algebra tools and numerical calculations, proposed recently in Refs. 1–3, the nonperturbative vacuum polarization effects in the 2+1D supercritical Dirac–Coulomb system with $Z>Z_{\mathrm{\text{cr}},1}$ are explored. Both the vacuum charge density ${\rho }_{\mathrm{\text{V P}}}(\overrightarrow{r})$ and vacuum energy ${{ℰ}}_{\mathrm{\text{V P}}}$ are considered. The main result of the work is that in the overcritical region ${{ℰ}}_{\mathrm{\text{V P}}}$ turns out to be a rapidly decreasing function $\sim -{\eta }_{\mathrm{\text{eff}}}{Z}^3/R$ with ${\eta }_{\mathrm{\text{eff}}}>0$ and $R$ being the size of the external Coulomb source. Due to a lot of details of calculation the whole work is divided into two parts I and II. In the present part I, we consider the evaluation and behavior of the vacuum density ${\rho }_{\mathrm{\text{V P}}}$, which further is used in part II for evaluation of the vacuum energy, with emphasis on the renormalization, convergence of the partial expansion for ${\rho }_{\mathrm{\text{V P}}}$ and behavior of the integral induced charge $Q_{\mathrm{\text{V P}}}$ in the overcritical region.

Nonperturbative vacuum polarization effects are explored for a supercritical Dirac–Coulomb system with $Z>Z_{\mathrm{\text{cr}},1}$ in 2+1D, based on the original combination of analytical methods, computer algebra and numerical calculations, proposed recently in Refs. 1–3. Both the vacuum charge density ${\rho }_{\mathrm{\text{V P}}}(\overrightarrow{r})$ and vacuum energy ${{ℰ}}_{\mathrm{\text{V P}}}$ are considered. Due to a lot of details of calculation the whole work is divided into two parts I and II. Taking account of results, obtained in the part I⁴ for ${\rho }_{\mathrm{\text{V P}}}$, in the present part II, the evaluation of the vacuum energy ${{ℰ}}_{\mathrm{\text{V P}}}$ is investigated with emphasis on the renormalization and convergence of the partial expansion for ${{ℰ}}_{\mathrm{\text{V P}}}$. It is shown that the renormalization via fermionic loop turns out to be the universal tool, which removes the divergence of the theory both in the purely perturbative and essentially nonperturbative regimes of the vacuum polarization. The main result of calculation is that for a wide range of the system parameters in the overcritical region ${{ℰ}}_{\mathrm{\text{V P}}}$ turns out to be a rapidly decreasing function $\sim -{\eta }_{\mathrm{\text{eff}}}{Z}^3/R$ with ${\eta }_{\mathrm{\text{eff}}}>0$ and $R$ being the size of the external Coulomb source. To the end the similarity in calculations of ${{ℰ}}_{\mathrm{\text{V P}}}$ in 2+1 and 3+1D is discussed, and qualitative arguments are presented in favor of the possibility for complete screening of the classical electrostatic energy of the Coulomb source by the vacuum polarization effects for $Z\gg Z_{\mathrm{\text{cr}},1}$ in 3+1D.