Annotation of the results obtained in 2021
Two-point singular functions of the QED of a strong field for a weakly inhomogeneous electric field between the plates of a plane capacitor, which are at a sufficiently large distance from each other, are constructed and studied. Complete sets of in- and out- solutions of the Dirac equation are found in terms of the light cone variables. With the help of these solutions, integral representations in the Fock-Schwinger proper time are constructed for all singular functions, which provide non-perturbative (with respect to the external field) calculations of transition amplitudes and average values of physical quantities. The article describing the results was accepted for publication [A.I. Breev, S.P. Gavrilov, D.M. Gitman, ZhETF, vol. 161, no. 2, 1 (2022); arXiv:1903.06832]. For the development of nonperturbative QED methods, testing of numerical methods adapted to describe the effects of strong fields, it is necessary to form a wider base of exact solutions of the Dirac equation. Such new in- and out-sets of solutions are obtained for an electric pulse, which is an infinitely smooth function with asymmetric on and off branches. The characteristics of the vacuum instability are calculated for different modes of switching on and off the pulse. [A.I. Breev, S.P. Gavrilov, D.M. Gitman, and A. A. Shishmarev, Phys. Rev. D 104, 076008 (2021); https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.076008?ft=1 ]. The production from vacuum of neutral fermion-antifermion pairs with anomalous magnetic moment under the action of an inhomogeneous magnetic field is studied. It is shown that for particles with a certain spin projection, the problem is reduced to the problem of the production of pairs of charged particles by an electric field given by a step-type potential. Using solutions of the Dirac-Pauli equation for a magnetic field specified in the form of a hyperbolic tangent of the coordinate we calculate the differential average number of produced pairs, the flux density of the number of produced particles, and the fluxes of energy and magnetic moment of the produced particles. It is shown that a flow in one direction is formed from flows of particles and antiparticles of equal intensity and with the same magnetic moments parallel to the external field. The back reaction leads to a smoothing of the inhomogeneity of the magnetic field. The effect may be of interest for the physics of neutrinos and dark matter. An article describing these results is accepted at Journal of High Energy Physics [T. C. Adorno, Zi-Wang He, S. P. Gavrilov, D. M. Gitman, JHEP (2021); arXiv: 2109.06053]. A representation of the Dirac model in Fock space for the interaction of photons with Dirac fermions of graphene in the presence of a strong slowly varying electric field, which violates the stability of the vacuum, is constructed. This representation accurately takes into account the effects of vacuum instability caused by electric fields, and the interaction of electrons and photons is taken into account perturbatively. In the lowest order of the perturbation theory in the interaction with photons, a relation is obtained that connects the total probability of radiation from any given state with the average value of the operator of the number of photons ("optical theorem"). Using this theorem, we calculated and analyzed the frequency and angular characteristics of radiation accompanying the flow of a direct current near the Dirac point in graphene in the first order of perturbation theory with respect of the interaction with photons. The characteristics of radiation from the one-electron state and from the vacuum state are compared, and an estimate is given of the possible observation of these types of radiation for such an external field. An article describing these results is still being prepared (to be posted on http://arxiv.org/ in January of 2022) and sent for publication in Physical Review D). The problem of the motion of a massless Dirac particle in the Coulomb field of a point charge is investigated. All Dirac Hamiltonians are constructed and their spectral analysis is performed for quasiparticles in graphene with a zero gap in the presence of a Coulomb impurity. A spectral analysis of the Dirac Hamiltonians is carried out and generalized eigenfunctions are calculated for any value of the impurity charge. The results obtained are used to study the local density of states in graphene in the vicinity of the Coulomb impurity, taking into account the ambiguity of the definition of the Dirac Hamiltonian. A.I. Breev, D.M. Gitman J. Exp. Theor. Phys. 132, 941 (2021); https://link.springer.com/article/10.1134%2FS1063776121060017 ]. The representation of the causal propagator of Dirac particles interacting with electromagnetic fields and weakly interacting with matter fields is obtained as a functional integral. The resulting effective gauge invariant action is interpreted as the pseudo-classical action of Dirac particles. Quantization of this action leads to the Dirac equation in background fields. The functional integral representation allows one to efficiently calculate the propagator and the arising quantum currents. The results are published in the article [D.M. Gitman, D.A. Ivanov, A.F. de Souza, European Physical Journal Plus, 136, 984 (2021); https://link.springer.com/article/10.1140%2Fepjp%2Fs13360-021-01982-z ].

 

Publications

---

Annotation of the results obtained in 2019
The regularization and renormalization procedure for quasi-local physical values such as the vector of electric current and the energy-momentum tensor of created particles is developed for a recently formulated nonperturbative approach in quantum electrodynamics (QED) which allows to study the effects of intense nonuniform electric field given by a step potential. We demonstrated that the regularization parameter used in this approach is uniquely determined by the duration of the observation procedure of the particle flows leaving the field region into the surrounding vacuum. It is shown that the proposed regularization procedure is sufficient to correctly formulate the problems where the interaction with the radiation field is taken into account along with the nonperturbative effects of the external field. We obtained a new consistency condition for a constant field model that takes into account a finite field length. The obtained condition defines a much wider range of applicability than the one established for a uniform field. An article describing this result is published as an electronic preprint https://arxiv.org/abs/1906.08801 and submitted to Physical Review D. In the framework of the same approach we constructed and studied exactly solvable model with a nonuniform field decreasing from its maximum value according to the inverse square law. In addition, the case of a composite weakly inhomogeneous wide field that rapidly decreases according to the inverse square law on asymptotics was studied. We found the complete sets of solutions of the Klein-Gordon-Fock and Dirac equations, and calculated the processes of scattering and particle production from vacuum for these fields. It was shown that the composite field reduces the contribution of switching on and off (boundary) effects to the mean number of particles produced and is therefore a more convenient starting approximation for calculating corrections to the local-constant field approximation. An article describing this result was published as an electronic preprint https://arxiv.org/abs/1911.09809 and submitted to The European Physical Journal C. All Dirac Hamiltonians as self-adjoint extensions of the initial Dirac operator for quasiparticles in graphene are constructed near the Coulomb impurity. The spectra and their (generalized) eigenfunctions of the Hamiltonians describing charge carriers in graphene in low-energy approximation are found. In each region of change of the impurity charge the corresponding spectral equations are obtained, and their numerical solutions are studied. Numerical solutions of the exact spectral equations for the regularized Coulomb impurity potential at small distances are studied. The exact equation for determining supercritical charges corresponding to bound states at the lowest energy level is found. An article describing this result is published as an electronic preprint https://arxiv.org/abs/1912.01322 and accepted for publication in Journal of Experimental and Theoretical Physics. The origin of superstrong magnetic fields in some neutron stars, called magnetars, is still an unresolved issue in modern astrophysics. We have constructed a model to explain the appearance of strong magnetic fields in compact stars based on chiral magnetic phenomena. We have found the conditions for the instability of a magnetic field at the border between the crust and the outer core in neutron stars. It is shown that the magnetic field can be amplified to the strength observed in magnetars. https://iopscience.iop.org/article/10.1088/1475-7516/2019/06/053

 

Publications

---

Annotation of the results obtained in 2020
The detailed procedure, that allows one to connect vacuum matrix elements of quasilocal operators of physical values with observables, is spelled out in the framework of QED with intense non-uniform electric fields specified by step potentials. Procedures for volumetric regularization and renormalization, which make it possible to calculate and distinguish the physical parts of various matrix elements of the current operator and the energy-momentum tensor while simultaneously relating them to the characteristics of the vacuum instability, are proposed. A modified scalar product for the solutions of the Dirac equation in a field specified by a step potential, with a regularization parameter, which is fixed from physical considerations, is introduced. It is shown that in the Klein zone this parameter is the time of observation of fluxes of produced particles emerging from the field region into the surrounding vacuum. It is demonstrated that the regularization procedure is sufficient for the correct formulation of problems in which, along with the nonperturbative effects of the external field, the interaction with the radiation field is taken into account. New self-consistency condition for a constant field model taking into account its final length is obtained. It is demonstrated that the latter condition define a much wider range of applicability than that established for a uniform field. The results are published in the article [S.P. Gavrilov and D.M. Gitman, Eur. Phys. J. C 80 820 (2020), https://link.springer.com/article/10.1140/epjc/s10052-020-8337-4 ]. Using the developed procedure, a representation of the Dirac model in the Fock space for the interaction of photons with Dirac fermions in the presence of a constant inhomogeneous electric field violating vacuum stability is constructed. The interaction representation, which takes into account the effects of vacuum instability caused by electric fields specified by a step potential exactly, is constructed as well. The interaction of electrons and photons is taken into account by perturbation theory. Within the framework of the Dirac model, which takes into account the interaction with a quantized electromagnetic field in the first order of the perturbation theory, a number of processes occurring in a monolayer graphene under the action of strong nonstationary electric fields are considered. The effects of the external field are taken into account nonperturbatively. An significant development of the kinetic equation formalism is presented. Quantum kinetic equations describing the emission of photons from electron-hole plasma generated from a vacuum by an electric field are derived from first principles. Approximate solutions of these equations are found for a self-consistent kinetic theory of electron, hole and photon generation and evolution under the action of a uniform time-dependent external electric field, adapted for the conditions of graphene. A number of concrete results obtained for photons emitted at small angles to the graphene plane. A characteristic anisotropy of the spectrum of the emitted photons and the appearance in this radiation of even harmonics of the external field, which can be observed, are discovered. The results are published in the article [S.P. Gavrilov, D.M. Gitman, V.V. Dmitriev, A.D. Panferov, and S.A. Smolyansky, Universe 2020, 6, 205, https://www.mdpi.com/2218-1997/6/11/205]. A locally constant field approximation for calculation of mean vacuum values of the current vector and energy-momentum tensor in QED with arbitrary weakly nonuniform step-type electric fields is obtained. Contributions to mean vacuum values of the current vector and energy-momentum tensor due to polarization (local) and those connected to pair creation effect (global) are calculated. The connection with similar representations of the effective Schwinger action is established. An article on the results of this study is being prepared for publication in Physical Review D. In addition to the 2019 report, we note that the results of an exactly solvable model with an inhomogeneous field decreasing from the maximum value according to the inverse square law were published in the article [T.C. Adorno, S.P. Gavrilov, and D.M. Gitman, Eur. Phys. J. C 80 88 (2020), https://link.springer.com/article/10.1140/epjc/s10052-020-7646-y ]. The problem of the motion of a massless Dirac particle in the Coulomb field of a point charge is investigated. All Dirac Hamiltonians are constructed and their spectral analysis is performed for quasiparticles in graphene with a zero gap in the presence of a Coulomb impurity. A spectral analysis of the Dirac Hamiltonians is carried out and generalized eigenfunctions are calculated for any value of the impurity charge. The obtained results are used to study the local density of states in graphene in the vicinity of the Coulomb impurity, taking into account the ambiguity of the definition of the Dirac Hamiltonian. An article on the results of this research is being prepared for publication in the Journal of Experimental and Theoretical Physics. The influence of the effects of vacuum polarization in a constant uniform magnetic field on the spectrum of the hydrogen atom is studied. It is shown that the finite energy levels of a hydrogen atom in a strong magnetic field, taking into account the vacuum polarization, can be obtained from the effective Heisenberg-Euler action in the local approximation. Here the strong background field acts as a «regularizer» of the Coulomb field, and the latter becomes finite at the origin. The results are published in [T. C. Adorno, D. M. Gitman, and A. E. Shabad, Universe 6, 204 (2020), https://www.mdpi.com/2218-1997/6/11/204 ]. Chiral fermions, electroweakly interacting with the background matter, which has an inhomogeneous density and velocity which depend arbitrarily on the coordinates, are studied. The dynamics of this system is described approximately by finding the Berry phase. An effective action is obtained and kinetic equations for right and left particles are derived. In the case of rotating matter, corrections for the anomalous electric current and the Adler anomaly are obtained. Some astrophysical applications are studied. Assuming that the chiral imbalance of a rotating neutron star disappears, the rate of change in magnetic helicity due to the interaction of chiral electrons with background neutrons is obtained. It turned out that the characteristic time of the helicity change coincides with the period of the magnetic cycle of some pulsars. These results are published in the article [M.S. Dvornikov, Nucl. Phys. B, 955, 115049 (2020), https://www.sciencedirect.com/science/article/pii/S0550321320301358 ].

 

Publications

---