Stability of QED Vacuum and 3+1 Dimensional Scattering Problem in the Presence of a Coulomb Scalar Potential and Vector Field

We show that, in the presence of a scalar field the range of the value of external field parameters a and b, at which corresponding Hamiltonian operator is hermitian, essentially wider than in its absence. It allows us to study precisely the question on stability of QED vacuum in the presence of a strong electric field of a point charge Z|e| and external scalar Coulomb field with respect to electron-positron pair production. Also, we consider the scattering of Dirac particle by the specified fields in 3+1 dimensions. The phase shift and wave functions are obtained exactly. We calculate the scattering amplitude in a quasi-classical approximation as a partial wave series. By means of figures obtained for the cross section σ(θ) in general and special cases, such as a≠b and a=b, we find that σ(θ) is not exactly symmetric about θ=π.     

A symmetry relating certain processes in 2-and 4-dimensional space-times and the value α0 = 1/4π of the bare fine structure constant

The symmetry manifests itself in exact relations between the Bogoliubov coefficients for processes induced by an accelerated point mirror in 1 + 1 dimensional space and the current (charge) densities for the processes caused by an accelerated point charge in 3 + 1 dimensional space. The spectra of pairs of Bose (Fermi) massless quanta emitted by the mirror coincide with the spectra of photons (scalar quanta) emitted by the electric (scalar) charge up to the factor e ²/ħc. The integral relation between the propagator of a pair of oppositely directed massless particles in 1 + 1 dimensional space and the propagator of a single particle in 3 + 1 dimensional space leads to the equality of the vacuum-vacuum amplitudes for the charge and the mirror if the mean number of created particles is small and the charge e = √ħc. Due to the symmetry, the mass shifts of electric and scalar charges (the sources of Bose fields with spin 1 and 0 in 3 + 1 dimensional space) for the trajectories with a subluminal relative velocity β₁₂ of the ends and the maximum proper acceleration w ₀ are expressed in terms of the heat capacity (or energy) spectral densities of Bose and Fermi gases of massless particles with the temperature w ₀/2π in 1 + 1 dimensional space. Thus, the acceleration excites 1-dimensional oscillation in the proper field of a charge, and the energy of oscillation is partly deexcited in the form of real quanta and partly remains in the field. As a result, the mass shift of an accelerated electric charge is nonzero and negative, while that of a scalar charge is zero. The symmetry is extended to the mirror and charge interactions with the fields carrying spacelike momenta and defining the Bogoliubov coefficients α^B,F. The traces trα^B,F, which describe the vector and scalar interactions of the accelerated mirror with a uniformly moving detector, were found in analytic form for two mirror trajectories with subluminal velocities of the ends. The symmetry predicts one and the same value e ₀ = √ħc for the electric and scalar charges in 3 + 1 dimensional space. Arguments are adduced in favor of the conclusion that this value and the corresponding value α₀ = 1/4π of the fine structure constant are the bare, nonrenormalized values. The text was submitted by the author in English.     

The effective two-loop Euler-Heisenberg action for scalar and spinor QED in a general constant background field

Using the Wordline formalism of QED we compute the two-loop effective action induced by a charged scalar, respectively spinor particle in a general constant electromagnetic field.     

Theory for the calculation of the force characteristics of an electromagnetic suspension of a superconducting body

A theory based on the method of secondary sources is developed for the calculation of the magnetic field and the force characteristics of electromagnetic suspension. This method leads to a system of Fredholm vector integral equations of the second kind in the density of the secondary sources, whose solution gives the surface currents in the superconducting bodies and then by a simple integration, the magnetic field and the force characteristics of the suspension. It is shown how the problem can be reformulated to apply it to the determination of the scalar secondary sources (magnetic charges), leading to integral equations of lower dimension. Examples are given for the calculation of scalar secondary sources for a superconducting half-space and a cylinder. Zh. Tekh. Fiz. 67, 3–9 (January 1997)     

Large-scale magnetic fields from inflation due to a <Emphasis Type="Italic">CPT</Emphasis>-even Chern–Simons-like term with Kalb–Ramond and scalar fields

We investigate the generation of large-scale magnetic fields due to the breaking of the conformal invariance in the electromagnetic field through the CPT-even dimension-six Chern–Simons-like effective interaction with a fermion current by taking account of the dynamical Kalb–Ramond and scalar fields in inflationary cosmology. It is explicitly demonstrated that magnetic fields on 1 Mpc scale with the field strength of ∼10⁻⁹ G at the present time can be induced.     

Vacuum polarization around an Aharonov-Bohm solenoid

The quantisation of a charged scalar field in an externally specified electromagnetic field, described by the vector potentialA _i=∂_if withf(t,r,θ,z)=Bθ is discussed. The electromagnetic field is zero everywhere except at the origin; a singular magnetic field (Aharonov-Bohm field) exists at the origin. The vacuum polarization around such a magnetic field is computed and the non-local behaviour is discussed.     

Entropic Corrections to Coulomb’s Law

Two well-known quantum corrections to the area law have been introduced in the literatures, namely, logarithmic and power-law corrections. Logarithmic corrections, arises from loop quantum gravity due to thermal equilibrium fluctuations and quantum fluctuations, while, power-law correction appears in dealing with the entanglement of quantum fields in and out the horizon. Inspired by Verlinde’s argument on the entropic force, and assuming the quantum corrected relation for the entropy, we propose the entropic origin for the Coulomb’s law in this note. Also we investigate the Uehling potential as a radiative correction to Coulomb potential in 1-loop order and show that for some value of distance the entropic corrections of the Coulomb’s law is compatible with the vacuum-polarization correction in QED. So, we derive modified Coulomb’s law as well as the entropy corrected Poisson’s equation which governing the evolution of the scalar potential ϕ. Our study further supports the unification of gravity and electromagnetic interactions based on the holographic principle.     

Implicit regularization beyond one-loop order: gauge field theories

We extend a constrained version of implicit regularization (CIR) beyond one-loop order for gauge field theories. In this framework, the ultraviolet content of the model is displayed in terms of momentum loop integrals order by order in perturbation theory for any Feynman diagram, while the Ward–Slavnov–Taylor identities are controlled by finite surface terms. To illustrate, we apply CIR to massless abelian gauge field theories (scalar and spinorial QED) to two-loop order and calculate the two-loop beta-function of spinorial QED. PACS  11.10.Gh; 11.15.Bt; 11.15.-q     

Spinor Relativity

Spinor relativity is a unified field theory, which derives gravitational and electromagnetic fields as well as a spinor field from the geometry of an eight-dimensional complex and ‘chiral’ manifold. The structure of the theory is analogous to that of general relativity: it is based on a metric with invariance group GL(ℂ²), which combines the Lorentz group with electromagnetic U(1), and the dynamics is determined by an action, which is an integral of a curvature scalar and does not contain coupling constants. The theory is related to physics on spacetime by the assumption of a symmetry-breaking ground state such that a four-dimensional submanifold with classical properties arises. In the vicinity of the ground state, the scale of which is of Planck order, the equation system of spinor relativity reduces to the usual Einstein and Maxwell equations describing gravitational and electromagnetic fields coupled to a Dirac spinor field, which satisfies a non-linear equation; an additional equation relates the electromagnetic field to the polarization of the ground state condensate.     

The dynamical mixing of light and pseudoscalar fields

We solve the general problem of mixing of electromagnetic and scalar or pseudoscalar fields coupled by axion-type interactions L _int = g _ϕ ϕε _μναβ F ^μν F ^αβ . The problem depends on several dimensionful scales, including the magnitude and direction of background magnetic field, the pseudoscalar mass, plasma frequency, propagation frequency, wave number, and finally the pseudoscalar coupling. We apply the results to the first consistent calculations of the mixing of light propagating in a background magnetic field of varying directions, which show a great variety of fascinating resonant and polarization effects.      

The energy—momentum tensor, the trace identity and the Casimir effect

The trace identity associated with the scale transformation x^Μ → x′^Μ = e^-ρx^Μ on the Lagrangian density for the noninteracting electromagnetic field in the co-variant gauge is shown to be violated on a single plate on which the Dirichlet boundary conditionA ^Μ(t, x¹, x², x³ = -a) = 0 is imposed. It is however respected in free space, i.e. in the absence of the plate. These results reinforce our assertions in an earlier paper where the same exercise was carried out using the Lagrangian density for the free, massive, real scalar field in 2 + 1 dimensions.     

Higher-dimensional perfect fluids and empty singular boundaries

In order to find out whether empty singular boundaries can arise in higher dimensional Gravity, we study the solution of Einstein’s equations consisting in a (N + 2)-dimensional static and hyperplane symmetric perfect fluid satisfying the equation of state ρ = ηp, being η an arbitrary constant and N ≥ 2. We show that this spacetime has some weird properties. In particular, in the case η > −1, it has an empty (without matter) repulsive singular boundary. We also study the behavior of geodesics and the Cauchy problem for the propagation of massless scalar field in this spacetime. For η > 1, we find that only vertical null geodesics touch the boundary and bounce, and all of them start and finish at z = ∞; whereas non-vertical null as well as all time-like ones are bounded between two planes determined by initial conditions. We obtain that the Cauchy problem for the propagation of a massless scalar field is well-posed and waves are completely reflected at the singularity, if we only demand the waves to have finite energy, although no boundary condition is required.     

Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field

We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantized electromagnetic field are described by minimal coupling, p→p−e A (x), where A(x) is the electromagnetic vector potential with an ultraviolet cutoff. If the interactions between the electrons and the quantized radiation field are turned off, the atom or molecule is assumed to have at least one bound state. We prove that, for sufficiently small values of the fine structure constant α, the interacting system has a ground state corresponding to the bottom of its energy spectrum. For an atom, we prove that its excited states above the ground state turn into metastable states whose life-times we estimate. Furthermore the energy spectrum is absolutely continuous, except, perhaps, in a small interval above the ground state energy and around the threshold energies of the atom or molecule. Received: 3 September 1998 / Accepted: 17 March 1999     

QED effective action in a constant electromagnetic field under conditions of possible Lorentz invariance violation in the Dirac equation

This paper is devoted to the calculation of corrections to QED effective action associated with the axial-vector condensate b ^μ, which violate the Lorentz invariance. It was shown that the linear in b ^μ contribution to the 1-loop effective action (Chern-Simons term) is absent in the case of a constant electromagnetic field. The contribution, which is quadratic in b ^μ, was calculated for the cases of both constant magnetic and electric fields. Asymptotic estimates of the quadratic in b ^μ term for strong and weak field strengths were obtained.     

Dark Energy Model with Canonical Scalar Field and Non-Linear Born–Infeld Type Scalar Field

In this paper, we propose the non-linear Born–Infeld scalar field and canonical scalar field dark energy models with the potential , which admits late time de Sitter attractor solution. The attractor solution corresponds to an equation of state ω_φ → − 1 and a cosmic density parameter Ω_φ → 1, which are important features for a dark energy model that can meet the current observations. dark energy; canonical scalar field, non-linear Born–Infeld type scalar field, attractor solution. PACS number(s):98.80.-k; 98.80.Cq; 98.80.Es.     

Investigation of Green's functions in an external electromagnetic field by the eigenfunction method

This paper contains a study of Green's functions in a quantum electrodynamics (QED) with an external electromagnetic field that disrupts vacuum stability. Representations are found for the Green's functions of a scalar QED in the eigenfunction basis of Klein-Gordon equations for a uniform constant electromagnetic field in combination with the field of a plane wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 70–74, June, 1989.     

Natural brane-confinement from massive Z 2-spontaneously broken Kaluza-Klein excitations in the bulk

For a real scalar field minimally coupled to bulk gravity, in five dimensions, we analytically solve the Gordon equation, near one of the degenerated vacua of an effective potential with a spontaneously broken Z ₂-symmetry. Dealing with the back-reaction from the excited massive modes on the whole scale function, we are pointing out that the lighter excitations of the scalar in the bulk turn more and more the warp function into the one of a partition on the confined brane.      

Inertial Mass and Vacuum Fluctuations in Quantum Field Theory

Motivated by recent works on the origin of inertial mass, we revisit the relationship between the mass of charged particles and zero-point electromagnetic fields. To this end we first introduce a simple model comprising a scalar field coupled to stochastic or thermal electromagnetic fields. Then we check if it is possible to start from a zero bare mass in the renormalization process and express the finite physical mass in terms of a cut-off. In scalar QED this is indeed possible, except for the problem that all conceivable cut-offs correspond to very large masses. For spin-1/2 particles (QED with fermions) the relation between bare mass and renormalized mass is compatible with the observed electron mass and with a finite cut-off, but only if the bare mass is not zero; for any value of the cut-off the radiative correction is very small.     

Conformal gauges and renormalized equations of motion in massless quantum electrodynamics

A formulation of massless QED is studied with a non-singular Lagrangian and conformal invariant equations of motion. It makes use of non-decomposable representations of the conformal groupG and involves two dimensionless scalar fields (in addition to the conventional charged field and electromagnetic potential) but gauge invariant Green functions are shown to coincide with those of standard (massless) QED. Assuming that the (non-elementary) representation ofG for the 5-potential which leaves the equations of motion invariant and leads to the free photon propagator of Johnson-Baker-Adler (JBA) conformal QED remains unaltered by renormalization, we prove that consistency requirements for conformal invariant 2-, 3-, and 4-point Green functions satisfying (renormalized) equations of motion and standard Ward identities lead to either a trivial solution (withe=0) or to a subcanonical dimensiond=1/2 for the charged field.To the memory of Kurt Symanzik     

An Exact Inflationary Solution to Non-Minimally Coupling

We find a new exact inflationary solution to non-minimally coupled scalar field from a specific H(φ). The inflation is driven by the evolution of the scalar field with a new inflation potential. The spectral index of the scalar density fluctuations n _s is consistent with the result of WMAP3 for the power-law flat ΛCDM model. Our solution relaxes the constraint to the quartic coupling constant, e.g. when ξ=10³, λ≤8.9×10⁻¹¹.