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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]

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]

In this paper, we analyze the fermionic condensate (FC) and the vacuum expectation value (VEV) of the energy–momentum tensor associated with an iso-spin- 1 ∕ 2 charged massive fermionic field induced by the presence of a S U (2) vortex, taking into account the effect of the conical geometry produced by this object. We consider the vortex as an idealized topological defect, i.e. very thin, straight and carrying a magnetic flux running along its core. Besides the direct coupling of the fermionic field with the iso-vector gauge field, we also admit the coupling with the scalar sector of the non-Abelian vortex system, expressed as a vector in the three-dimensional iso-space. Due to this interaction, the FC is expressed as the sum of two contributions associated with the two different effective masses for the ± 1 ∕ 2 fermionic components of the iso-spin operator, τ 3 ∕ 2. The VEV of the energy tensor also presents a similar structure. The vacuum energy density is equal to the radial and axial stresses. As to the azimuthal one, it is expressed in terms of the radial derivative of energy density. Regarding the magnetic flux, both the FC and the VEV of the energy–momentum tensor can be positive or negative. Another interesting consequence of the interaction with the bosonic sector, the FC and VEV of the energy–momentum tensor, presents different intensity for different values of the ratio between the scalar coupling constant and the mass of the fermionic field. This is a new feature presented by the system. [ABSTRACT FROM AUTHOR]

We review recent progress in the computation of leading quantum corrections to the energies of classical solitons with topological structure, including multi-soliton models in one space dimension and string configurations in three space dimensions. Taking advantage of analytic continuation techniques to efficiently organize the calculations, we show how quantum corrections affect the stability of solitons in the Shifman–Voloshin model, stabilize charged electroweak strings coupled to a heavy fermion doublet, and bind Nielsen–Olesen vortices at the classical transition between type I and type II superconductors. [ABSTRACT FROM AUTHOR]

Operator-product expansion (OPE) can be employed to obtain the lowest-order, nonlocal quark scalar condensate component of gluon vacuum polarization. In particular, the nonlocal quark scalar condensate can be calculated by solving the Dyson–Schwinger equation (DSE) of QCD. Then, field-theoretical aspects of the gluon vacuum polarization and nonperturbative gluon propagator are considered in the Landau gauge. The gluon propagator we obtained is finite in the infrared domain, where the single gluon mass m g can be determined. Our results for the m g / Λ QCD ratio range of that from 1.32 to 1.36, which agrees with previous determinations for this ratio. Then, the analytic structure of the gluon propagators from the OPE results is explored. The analysis of the gluon Schwinger function finds clear evidence of the positivity violations in the gluon propagator. In addition, the results of replacing the OPE simplified quark loop with the full quark one-loop are calculated in vacuum to investigate how good the OPE approximation approach is. The results demonstrate that the OPE approach provides a good approximate method to calculate the full light (u / d) quark loop in vacuum. In particular, the OPE approach can well approximate the approach with full quark one-loop in a specific model. Finally, a new method for obtaining the chemical potential dependence of the gluon vacuum polarization and the dressed gluon propagators is developed. [ABSTRACT FROM AUTHOR]

In this paper, we give an update on divergent problems concerning the radiative corrections of quantum electrodynamics in (3 + 1) dimensions. In doing so, we introduce a geometric adaptation for the covariant photon propagator by including a higher derivative field. This derivation, so-called generalized quantum electrodynamics, is motivated by the stability and unitarity features. This theory provides a natural and self-consistent extension of the quantum electrodynamics by enlarging the space parameter of spinor-gauge interactions. In particular, Haag's theorem undermines the perturbative characterization of the interaction picture due to its inconsistency on quantum field theory foundations. To circumvent this problem, we develop our perturbative approach in the Heisenberg picture and use it to investigate the behavior of the operator current at one-loop. We find the two- and three-point correlation functions are ultraviolet finite, electron self-energy and vertex corrections, respectively. On the other hand, we also explain how the vacuum polarization remains ultraviolet divergent only at e 2 order. Finally, we evaluate the anomalous magnetic moment, which allows us to specify a lower bound value for the Podolsky parameter. [ABSTRACT FROM AUTHOR]

In this paper, the versions of quantum electrodynamics (QED) with spinors in fermion equations are briefly examined. In the new variants of the theory, the concept of vacuum polarization is unnecessary. The new content of fermion vacuum (without the Dirac sea) in the examined versions of QED leads to new physical consequences, part of which can be tested experimentally in the future. [ABSTRACT FROM AUTHOR]

We investigate the cooling–heating phase transition of the Euler–Heisenberg-AdS black hole. First, the black hole thermodynamic quantities and the state equation are reviewed. Then, we research cooling–heating phase transition and further plot the inversion and isenthalpic curves in the T–P plane. Meanwhile, we find that the inversion temperature gradually decreases with the increase of Euler–Heisenberg parameter a for the inversion curves, while this parameter has no effect in the cooling region, and the isenthalpic curves gradually move to the positive direction of X-axis with the increase of Euler–Heisenberg parameter a in the heating region. In particular, the inversion temperature and pressure of this black hole are negative, we deem that this case is caused by the vacuum polarization and the quantum electrodynamics corrections, which makes the electromagnetic energy (repulsion force) produced by the black hole shield the gravity produced by the black hole mass. In addition, this explanation has been mentioned in previous studies [M. Daniela and B. Nora, Phys. Rev. D 102, 084011 (2020); R. Ruffini, Y. B. Wu and S. S. Xue, Phys. Rev. D 88, 085004 (2013)]. [ABSTRACT FROM AUTHOR]

We construct a new class of d -dimensional black hole solutions with Toroidal horizons in f (R) gravity framework which is surrounded by quintessence and string cloud configuration, whose asymptotic structures are determined by the quintessential state parameter ω q and dimension's parameter d. We point out that the asymptotic behavior of the obtained solutions is neither asymptotically flat nor (A)dS when we have ω q + 2 ω q + 1 > d and d ≤ 3. Regarding the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we investigate the critical behavior of our black hole solutions. In d = 3 and Q ≠ 0 , the P–V diagrams are more complex than that of the standard Van der Waals. These diagrams behave like the Born–Infeld-AdS P–V diagrams. When d = 3 and Q = 0 , the P–V diagrams behave like the standard Van der Waals system (In this work [S. Gunasekaran, D. Kubiznaak and R. B. Mann, Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization, J. High Energy Phys. (2012).] [S. Gunasekaran, D. Kubiznaak and R.B. Mann, Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization, J. High Energy Phys. (2012)], the authors believe that the BTZ black holes, contrary to the higher-dimensional case, do not show any critical behavior. In this work, we have showed that the three-dimensional (3D) black holes can also have critical behavior and coincide with those of the Van der Waals system). Besides, we have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form. We figure out the effect of the coupling constant λ , the string parameter b, and the quintessential state parameter ω q on the height of the potential barrier and the other thermodynamical quantities like temperature and heat capacity. Then, we study the quasinormal modes (QNMs) of 3D black holes in the f (R) context. For this purpose, we use the WKB approximation method upto third-order corrections. We have shown the perturbation's decay in corresponding diagrams when the string parameter b changes. [ABSTRACT FROM AUTHOR]

The problem of determining the main parameters of light nuclei from precision atomic spectroscopy is considered. Within the framework of the quasipotential method in quantum electrodynamics, the energy interval (2 S − 1 S) in muonic ions of lithium, beryllium and boron is calculated. Corrections of orders α 3 ÷ α 6 , which are determined by relativistic effects, effects of vacuum polarization, nuclear structure and recoil, as well as combined corrections, including the above, are taken into account. Nuclear structure effects are expressed in terms of the nuclear charge radius in the case of one-photon interaction and the electromagnetic form factors of nuclei in the case of two-photon interaction. The obtained numerical values for the (2 S − 1 S) interval can be used for comparison with future experimental data and for a more accurate determination of the nucleus charge radii. [ABSTRACT FROM AUTHOR]

The aim of this brief review is twofold. First, we give an overview of the unprecedented experimental efforts to measure the gravitational acceleration of antimatter; with antihydrogen, in three competing experiments at CERN (AEGIS, ALPHA and GBAR), and with muonium and positronium in other laboratories in the world. Second, we present the 21st Century's attempts to develop a new model of the Universe with the assumed gravitational repulsion between matter and antimatter; so far, three radically different and incompatible theoretical paradigms have been proposed. Two of these three models, Dirac–Milne Cosmology (that incorporates CPT violation) and the Lattice Universe (based on CPT symmetry), assume a symmetric Universe composed of equal amounts of matter and antimatter, with antimatter somehow "hidden" in cosmic voids; this hypothesis produced encouraging preliminary results. The heart of the third model is the hypothesis that quantum vacuum fluctuations are virtual gravitational dipoles; for the first time, this hypothesis makes possible and inevitable to include the quantum vacuum as a source of gravity. Standard Model matter is considered as the only content of the Universe, while phenomena usually attributed to dark matter and dark energy are explained as the local and global effects of the gravitational polarization of the quantum vacuum by the immersed baryonic matter. An additional feature is that we might live in a cyclic Universe alternatively dominated by matter and antimatter. In about three years, we will know if there is gravitational repulsion between matter and antimatter; a discovery that can forever change our understanding of the Universe. [ABSTRACT FROM AUTHOR]

In this work, we consider the generalized quantum electrodynamics proposed by Podolsky in Heisenberg picture via Källén methodology. We investigate the effects of higher-order derivatives to understand the qualitative and quantitative aspects of vacuum polarization. In addition, the most general structure of induced current and polarization tensor that emerge naturally by a perturbative scheme "à la" Källén is also obtained. Afterward, we discuss the physical implication of charge renormalization in the perspective of unitary and stable Podolsky theory. [ABSTRACT FROM AUTHOR]

We have previously shown that the singularity in a Schwarzschild black hole of stellar or larger mass may be avoided in a semiclassical manner by using as a source of gravity the stress-energy tensor (SET) corresponding to vacuum polarization of quantum fields, with a minimum spherical radius a few orders of magnitude larger than the Planck length. In this note we estimate the nonlocal contribution to the total SET due to particle creation from vacuum. We show that this contribution is negligibly small as compared to vacuum polarization and does not affect the previously suggested scenario. [ABSTRACT FROM AUTHOR]

We consider the gravity-induced effects associated with a massless scalar field living in a higher-dimensional spacetime being the tensor product of Minkowski space and spherically-symmetric space with angle deficit. These spacetimes are considered as simple models for a multidimensional global monopole or cosmic string with flat extra dimensions, where the deficit of solid angle is proportional to Newton constant and tension. Thus, we refer to them as conical backgrounds. In terms of the angular deficit value, we derive the perturbative expression for the scalar Green's function and compute it to the leading order. With the use of this Green's function we compute the renormalized vacuum expectation value of the scalar-field's energy-momentum tensor. We make some general note on the linear-on-curvature part of the trace of even coefficients of Schwinger-deWitt expansion. [ABSTRACT FROM AUTHOR]

We consider the effects of vacuum polarization and particle creation of a scalar field on Lie groups with a non-stationary bi-invariant metric of the Robertson–Walker type. The vacuum expectation values of the energy momentum tensor for a scalar field determined by the group representation are found using the noncommutative integration method for the field equations instead of separation of variables. The results obtained are illustrated by the example of the three-dimensional rotation group. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Scalar Quantum Electrodynamics is investigated in the Heisenberg picture via the Duffin-Kemmer-Petiau gauge theory. On this framework, a perturbative method is used to compute the vacuum polarization tensor and its corresponding induced current for the case of a charged scalar field in the presence of an external electromagnetic field. Charge renormalization is brought into discussion for the interpretation of the results for the vacuum polarization. [ABSTRACT FROM AUTHOR]

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 are explored. Both the vacuum charge density and vacuum energy are considered. The main result of the work is that in the overcritical region turns out to be a rapidly decreasing function with and 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 , which further is used in part II for evaluation of the vacuum energy, with emphasis on the renormalization, convergence of the partial expansion for and behavior of the integral induced charge in the overcritical region. [ABSTRACT FROM AUTHOR]

Nonperturbative vacuum polarization effects are explored for a supercritical Dirac-Coulomb system with 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 and vacuum energy 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 , in the present part II, the evaluation of the vacuum energy is investigated with emphasis on the renormalization and convergence of the partial expansion for . 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 turns out to be a rapidly decreasing function with and being the size of the external Coulomb source. To the end the similarity in calculations of 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 in 3+1D. [ABSTRACT FROM AUTHOR]

Nonperturbative vacuum polarization effects are explored for a supercritical Coulomb source with in 1+1D. Both the vacuum charge density and vacuum energy 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. [ABSTRACT FROM AUTHOR]

An analysis of the effects of the passage of a gravitational wave (GW) on the quantum vacuum is made within the context of the Nexus paradigm of quantum gravity. Results indicate that if the quantum vacuum includes electrically charged virtual particle fields, then a GW will induce vacuum polarization. The equations of General Relativity (GR) are then reformulated to include electric charge displacements in the quantum vacuum imposed by an anisotropic stress - momentum tensor. It is then demonstrated that as a result of the spacetime piezoelectric effect, a gravitational wave is associated with a rotating electromagnetic wave and that the converse effect produced by strong electromagnetic fields is responsible for the generation of relativistic jets and gamma ray bursts. Objects with strong electromagnetic fields will apparently violate the strong equivalence principle. [ABSTRACT FROM AUTHOR]

We compute the QCD coupling constant, , from the Adler function with vector hadronic vacuum polarization (HVP) function. On the lattice, Adler function can be measured by the differential of HVP at two different momentum scales. HVP is measured from the conserved-local vector current correlator using n f = 2 + 1 flavor Domain Wall lattice data with three different lattice cutoffs, up to a 3.14 GeV. To avoid the lattice artifact due to O(4) symmetry breaking, we set the cylinder cut on the lattice momentum with reflection projection onto vector current correlator, and it then provides smooth function of momentum scale for extracted HVP. We present a global fit of the lattice data at a justified momentum scale with three lattice cutoffs using continuum perturbation theory at to obtain the coupling in the continuum limit at arbitrary scale. We take the running to Z boson mass through the appropriate thresholds, and obtain ( M Z) = 0.1191(24)(37) where the first is statistical error and the second is systematic one. [ABSTRACT FROM AUTHOR]

We start with the well-known expression for the vacuum polarization and suitably modify it for 21-dimensional spin-orbit coupled (SOC) fermions on the low-buckled honey-comb structured lattice plane described by the low-energy Liu-Yao-Feng-Ezawa (LYFE) model Hamiltonian involving the Dirac matrices in the chiral representation obeying the Clifford algebra. The silicene and germanene fit this description suitably. They have the Dirac cones similar to those of graphene and SOC is much stronger. The system could be normal or ferromagnetic in nature. The silicene turns into the latter type if there is exchange field arising due to the proximity coupling to a ferromagnet (FM) such as depositing Fe atoms to the silicene surface. For the silicene, we find that the many-body effects considerably change the bare Coulomb potential by way of the dependence of the Coulomb propagator on the real-spin, iso-spin and the potential due to an electric field applied perpendicular to the silicene plane. The computation aspect of the Casimir-Polder force (CPF) needs to be investigated in this paper. An important quantity in this process is the dielectric response function (DRF) of the material. The plasmon branch was obtained by finding the zeros of DRF in the long-wavelength limit. This leads to the plasmon frequencies. We find that the collective charge excitations at zero doping, i.e., intrinsic plasmons, in this system, are absent in the Dirac limit. The valley-spin-split intrinsic plasmons, however, come into being in the case of the massive Dirac particles with characteristic frequency close to 10 THz. Our scheme to calculate the Casimir-Polder interaction (CPI) of a micro-particle with a sheet involves replacing the dielectric constant of the sample in the CPI expression obtained on the basis of the Lifshitz theory by the static DRF obtained using the expressions for the polarization function we started with. Though the approach replaces a macroscopic constant by a microscopic quantity, it has the distinct advantage of the many-body effect inclusion seamlessly. We find the result that for the nontrivial susceptibility and polarizability values of the sheet and micro-particle, respectively, there is crossover between attractive and repulsive behavior. The transition depends only on these response functions apart from the ratio of the film thickness and the micro-particle separation (/) and temperature. Furthermore, there is a longitudinal electric field induced topological insulator (TI) to spin-valley-polarized metal (SVPM) transition in silicene, which is also referred to as the topological phase transition (TPT). The low-energy SVP carriers at TPT possess gapless (massless) and gapped (massive) energy spectra close to the two nodal points in the Brillouin zone with maximum spin-polarization. We find that the magnitude of the CPF at a given ratio of the film thickness and the separation between the micro-particle and the film are greater at TPT than at the TI and trivial insulator phases. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Here we analyze the finite temperature expectation values of the charge and current densities for a massive fermionic quantum field with nonzero chemical potential , 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 is smaller than the mass of the field quanta . [ABSTRACT FROM AUTHOR]

We consider QED with strong external backgrounds that are concentrated in restricted space areas. The latter backgrounds represent a kind of spatial x-electric potential steps for charged particles. They can create particles from the vacuum, the Klein paradox being closely related to this process. We describe a canonical quantization of the Dirac field with x-electric potential step in terms of adequate in- and out-creation and annihilation operators that allow one to have consistent particle interpretation of the physical system under consideration and develop a nonperturbative (in the external field) technics to calculate scattering, reflection, and electron-positron pair creation. We resume the physical impact of this development. [ABSTRACT FROM AUTHOR]

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 , where is the electron mass. Finite temperature modification mainly comes through the hot fermions when . 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 as well as the electromagnetic properties of the background medium in the temperature range . 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, , 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. [ABSTRACT FROM AUTHOR]

In the standard model, stabilization of a classically unstable cosmic string may occur through the quantum fluctuations of a heavy fermion doublet. We review numerical results from a semiclassical expansion in a reduced version of the standard model. In this expansion, the leading quantum corrections emerge at one loop level for many internal degrees of freedom. The resulting vacuum polarization energy and the binding energies of occupied fermion energy levels are of the same order, and must therefore be treated on equal footing. Populating these bound states lowers the total energy compared to the same number of free fermions and assigns a charge to the string. Charged strings are already stabilized for a fermion mass only somewhat larger than the top quark mass. Though obtained in a reduced version, these results suggest that neither extraordinarily large fermion masses nor unrealistic couplings are required to bind a cosmic string in the standard model. Furthermore, we also review results for a quantum stabilization mechanism that prevents closed Nielsen-Olesen-type strings from collapsing. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2 + 1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization, for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions. [ABSTRACT FROM AUTHOR]

We propose a method of Casimir pressure renormalization for massive scalar field in a ball. This method is slightly different from the generally accepted methods. An alternative way of choosing the normalization point leads to an exponential pressure dependence on the mass of the field instead of an inverse polynomial dependence. The proposed method does not use the scalar quantized field in the exterior domain. This allows us to bypass the difficulties that appear when one uses the standard approach. [ABSTRACT FROM AUTHOR]