Annotation of the results obtained in 2017
A comparative study is carried out for the effects of particle-antiparticle pair creation from vacuum in the basic exactly solvable models with a time-dependent electric field, where this phenomenon is caused by a T-constant field, a Sauter type field and an exponential peak consisting of increasing and decreasing components, http://www.worldscientific.com/doi/abs/10.1142/S0217751X17501056 A number of new results have been obtained for the limiting values of parameters that determine the rate of switching the fields on and off, as well as the effective duration of switching. Thus, in the case of slowly varying fields, the mean number of pairs created by the T-constant field is found with accuracy up to the next-to-leading terms exhibiting oscillatory behavior. The momentum-dependence of the mean number of pairs created by an exponential field switching rapidly on and switching slowly off is studied in detail. For a slowly varying field of Sauter type, the density of the number of pairs created from vacuum in the strong-field regime is calculated. In the one-loop approximation, the mean values are obtained for the vacuum current and the energy-momentum tensor in a slowly varying Sauter type field, and in one or two slowly varying components of the exponential peak. This made it possible to establish the universal behavior of vacuum mean values of the densities for the number of created pairs, for the vacuum current, and for the energy-momentum tensor in slowly varying strong electric fields. The results obtained for the exponential peak field, https://elibrary.ru/download/elibrary_29032489_71836221.pdf https://link.springer.com/article/10.1007/s11182-017-1090-y https://link.springer.com/article/10.1007%2Fs11182-017-1133-4 demonstrate an enlargement of distributions for the number of pairs, both bosons and fermions, depending on the longitudinal momentum with increasing effective duration of the electric field, and also show an increase in the density of the pairs created in this case. A study is carried out on the on-off effects for a combination of a T-constant field and two types of exponential fields describing the stages of switching on and off [the report T.C. Adorno “Switching-on and switching-off effects of external fields in the vacuum instability” at the Lomonosov Conference on Elementary Particle Physics, 24–30 August, 2017, is accepted for publication in the Conference Proceedings; an article describing the results is being prepared for publication]. The scattering of particles and the creation of particle-antiparticle pairs in a uniformly directed electric field exponentially decreasing at both asymptotics along this axis and determined by independent gradients have been studied, https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.096020 A complete set of solutions to the Dirac and Klein–Gordon equations for such an external field is found. The scattering probabilities, the differential and integral mean numbers of created particles, and the probability of the vacuum to remain a vacuum are calculated. The effects of pair creation are studied for the three most interesting configurations: the small gradient case, the sharp peak case, and the essentially asymmetric case in which the gradients differ substantially in magnitude. The presented exactly solvable model made it possible for the first time to investigate the effects of pair creation for an essentially asymmetric field configuration. In particular, the conditions are established under which the contribution of a sharply varying peak component can be neglected, by considering only the contribution of an exponentially decreasing field. The sharp peak represents a new regularization of the Klein step associated with the known (seeming) Klein paradox. This regularization is compared with the regularization within the Sauter potential. In the case of equal gradients, the effects in the exponential peak field are compared with the effects known for potentials of the Sauter type and the L-constant field (the field between the capacitor plates). This permits us to study the role of edge effects in the creation of particle-antiparticle pairs. Along with the Sauter type and the L-constant field potentials, the presented exactly solvable model allows us to approximate, at least qualitatively, a wide class of realistic step-type potentials, such as those that form p-n transitions in graphene. This enables the development of new nonperturbative methods in the physics of graphene and other nanomaterials for which the conductivity can be described by the Dirac model. In the framework of a nonlocal quark model, a form factor has been calculated for the transition of a photon into three pions. In the local and chiral limits, this form factor is equal to the Wess–Zumino term caused by the chiral anomaly. This form factor presents the contribution of the hadronic polarization of the vacuum into the anomalous magnetic moment of the muon, https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.074025

 

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Annotation of the results obtained in 2015
Function of transition of photon into two charged pions was calculated in framework of contribution investigation in anomalous magnetic moment of moun from light by light processes in nonlocal quark model. One is described of pion charged form-factor in nonlocal model. “Density” function was obtained for contribution of anomalous magnetic momentum of muon from processes of light by light scattering. This asymptotic function have agreement of QCD on high energy and QCD-sum rule and current algebra on low energy. The contribution from hadronic polarization of vacuum was obtained in the null order on 1/Nc – color number. The taking of account of the first order of color number is significant. Experiment data also have a indication from electron-positron cross-section into pair of pions. We have studied quantum processes involving the effect of particle creation in the framework of strong-field quantum electrodynamics with t-electric potential steps. We provide some important and so far unpublished details of nonperturbative calculations for three exactly solvable cases: Sauter-like (or pulse) electric field, T-constant electric field, and exponentially decaying electric field. We show how these cases help to gain insight into the universal features of particle creation from vacuum. Using new strong-field QFT approach developed by us for x-electric potential steps, we consider particle scattering and vacuum instability in the so-called L-constant electric field, which is a constant electric field confined between two capacitor plates separated by a finite distance L. We obtain and analyze special sets of stationary solutions of the Dirac and Klein-Gordon equations with the L-constant electric field. Then, we represent probabilities of particle scattering and characteristics of the vacuum instability (related to the pair creation) in terms of the introduced solutions. From exact formulas, we derive asymptotic expressions for the differential mean numbers, for the total mean number of created particles, and for the vacuum-to-vacuum transition probability. Using the equivalence principle, we demonstrate that the distributions of created particles by L-constant electric field and gravitational field of a black hole have similar thermal structure. Information about project results of first year are located on http://tsu.ru/science/orntd/uchastie-v-konkursakh-rossiyskogo-nauchnogo- fonda/

 

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Annotation of the results obtained in 2016
The full set of solutions for Dirac and Klein-Gordon equations for two combinations of exponentional field (peak field) was found. This type of fields allows studying the effects of switching on and off with arbitrary speed of switching, described by two parametes. All the characteristics of pair creation from the vacuum by this field are studied, including the distribution of mean numbers of particles created (both fermions and scalar bosons) with respect to the momentum, full number of particles created and vacuum-to-vacuum transition probability. Different asymptotic regimes were studied in detail. It was shown that choice of the symmetric form of the peak leads to the pair creation effects similar to the case of pulsing Sauter-like or t-constant field. For the first time an asymmetric field configuration with significantly different speeds of switching on and off was studied. Such configuration provides an important generalization of exponentially decaying field and defines its lapplicability limits. The results obtained allows one to study the effects of field switching on and off both separately from each other and their combined effects. The possibility to select parameters enables to adapt the peak form to different realistic situations; in particular, it allows to imitate different field configurations typical of graphene, Weyl semimetals and other nanostuctures with the relativistic behavior of current carriers. The conditions when in- and out- Fock spaces of the QED with unstable vacuum in the presence of critical potential steps are unitarity equivalent were studied. It was shown that the linear canonical transformation(together with its adjoint transformation) is a proper one, if the full number of particles created from the vacuum is finite. The general density operator with the vacuum initial condition, describing the state deformed by external field, is constructed. The reductions of this state to electron and positron subsystems are obtained, and the loss of the information in these reductions is calculated as a corresponding entropy change is calculated. The general consideration is illustrated by studying the deformation of the quantum vacuum between two capacitor plates. The entanglement measures of these reduced density operators were found as von Neumann entropies. The study of one-loop contributions in the mean vacuum current in external intense nonuniform stationary electromagnetic field which is a combination of a Coulomb field of a finite-radius charge and an intense slowly-changing slightly inhomogeneous electromagnetic field. The nonlinear Maxwell equations up to the third order of intensive field variations are obtained, including QED with the effective Euler-Heisenberg action. The expressions for the corrections to Coulomb field, the total charge and the charge density via the derivatives of the effective Lagrangian for the field invariants were obtained in the approximation of a linear system response. The anisotropic distribution of the induced charge density inside and outside of external charge was found. It was shown that the result is significantly different from the case of absence of external electromagnetic field, as in framework of QED in 3+1 dimensional space-time or QED_{3,2} with the reduced dimension which is used to describe the dynamics in the graphene. The representation for the Dirac model of current carriers in Fock space for graphene monolayer at the low energies where the vacuum instability effects are taken into account precisely while the interaction between electrons and photons is considered via perturbation theory. The effective theory of a photon radiation by the electrons is considered in the leading order of perturbation, and the expressions for the full probabilities of photon radiation are obtained. The estimation of the applicability of the quasi-constant electric field model (when it is possible to neglect the effects of switching on and off) in the framework of the photon radiation by the electrons is given. Transition form-factor two photons into pair of charge or neutral pions was studied in framework of nonlocal quark model. This form-factor have a connection with polarizability of pion which was obtained in nonlocal quark model and a comparative analysis was carried out with previous results. Dipole moment of neutron was calculated based on CP – violation decay eta and eta-prime meson into pair of pions. Dipole moment of neutron was estimated with delta (1232) resonance and taking into account the new experimental data.

 

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