Effective energy-momentum tensor of strong-field QED with unstable vacuum

We study the influence of a vacuum instability on the effective energy-momentum tensor (EMT) of QED, in the presence of a quasiconstant external electric field, by means of the relevant Green functions. In the case when the initial vacuum, |0,in>, differs essentially from the final vacuum, |0,out>, we find explicitly and compared both the vacuum average value of EMT, , and the matrix element, . In the course of the calculation we solve the problem of the special divergences connected with infinite time T of acting of the constant electric field. The EMT of pair created by an electric field from the initial vacuum is presented. The relations of the obtained expressions to the Euler-Heisenberg's effective action are established.Comment: 8 pages, 1 figure, Talk given at "QFEXT'05", the 7-th workshop on quantum field theory under the influence of external conditions, Barcelona, Spain, Sept. 5-9, 2005; minor misprints correcte

Energy-momentum tensor in thermal strong-field QED with unstable vacuum

The mean value of the one-loop energy-momentum tensor in thermal QED with electric-like background that creates particles from vacuum is calculated. The problem differes essentially from calculations of effective actions (similar to that of Heisenberg--Euler) in backgrounds that do not violate the stability of vacuum. The role of a constant electric background in the violation of both the stability of vacuum and the thermal character of particle distribution is investigated. Restrictions on the electric field and its duration under which one can neglect the back-reaction of created particles are established.Comment: 7 pages, Talk presented at Workshop "Quantum Field Theory under the Influence of External Conditions", Leipzig, September 17-21, 2007; introduction extended, version accepted for publication in J.Phys.

Proper time and path integral representations for the commutation function

On the example of the quantized spinor field, interacting with arbitrary external electromagnetic field, the commutation function is studied. It is shown that a proper time representation is available in any dimensions. Using it, all the light cone singularities of the function are found explicitly, generalizing the Fock formula in four dimensions, and a path integral representation is constructed.Comment: 20 pages, LaTeX, uses pictex macro

Regularization, renormalization and consistency conditions in QED with x-electric potential steps

The present article is an important addition to the nonperturbative formulation of QED with x-steps presented by Gavrilov and Gitman in Phys. Rev. D. 93, 045002 (2016). Here we propose a new renormalization and volume regularization procedures which allow one to calculate and distinguish physical parts of different matrix elements of operators of the current and of the energy-momentum tensor, at the same time relating the latter quantities with characteristics of the vacuum instability. For this purpose, a modified inner product and a parameter {\tau} of the regularization are introduced. The latter parameter can be fixed using physical considerations. In the Klein zone this parameter can be interpreted as the time of the observation of the pair production effect. In the refined formulation of QED with x-steps, we succeeded to consider the backreaction problem. In the case of an uniform electric field E confined between two capacitor plates separated by a finite distance L, we see that the smallness of the backreaction implies a restriction (the consistency condition) on the product EL from above.Comment: 33 pages, version accepted for publication in Eur. Phys. J.

Vacuum instability in slowly varying electric fields

Nonperturbative methods have been well-developed for QED with the so-called t-electric potential steps. In this case a calculation technique is based on the existence of specific exact solutions (in and out solutions) of the Dirac equation. However, there are only few cases when such solutions are known. Here, we demonstrate that for t-electric potential steps slowly varying with time there exist physically reasonable approximations that maintain the nonperturbative character of QED calculations even in the absence of the exact solutions. Defining the slowly varying regime in general terms, we can observe a universal character of vacuum effects caused by a strong electric field. In the present article, we find universal approximate representations for the total density of created pairs and vacuum mean values of the current density and energy-momentum tensor that hold true for arbitrary t-electric potential steps slowly varying with time. These representations do not require knowledge of the corresponding solutions of the Dirac equation, they have a form of simple functionals of a given slowly varying electric field. We establish relations of these representations with leading terms of the derivative expansion approximation. These results allow one to formulate some semiclassical approximations that are not restricted by the smallness of differential mean numbers of created pairs.Comment: 37 pages, version accepted for publication in Phys. Rev. D. arXiv admin note: substantial text overlap with arXiv:1512.0128

One-loop energy-momentum tensor in QED with electric-like background

We have obtained nonperturbative one-loop expressions for the mean energy-momentum tensor and current density of Dirac's field on a constant electric-like background. One of the goals of this calculation is to give a consistent description of back-reaction in such a theory. Two cases of initial states are considered: the vacuum state and the thermal equilibrium state. First, we perform calculations for the vacuum initial state. In the obtained expressions, we separate the contributions due to particle creation and vacuum polarization. The latter contributions are related to the Heisenberg-Euler Lagrangian. Then, we study the case of the thermal initial state. Here, we separate the contributions due to particle creation, vacuum polarization, and the contributions due to the work of the external field on the particles at the initial state. All these contributions are studied in detail, in different regimes of weak and strong fields and low and high temperatures. The obtained results allow us to establish restrictions on the electric field and its duration under which QED with a strong constant electric field is consistent. Under such restrictions, one can neglect the back-reaction of particles created by the electric field. Some of the obtained results generalize the calculations of Heisenberg-Euler for energy density to the case of arbitrary strong electric fields.Comment: 35 pages; misprints in the sign in definitions (40)-(43), and (68) corrected, results unchange

On Quantization of Time-Dependent Systems with Constraints

The Dirac method of canonical quantization of theories with second class constraints has to be modified if the constraints depend on time explicitly. A solution of the problem was given by Gitman and Tyutin. In the present work we propose an independent way to derive the rules of quantization for these systems, starting from physical equivalent theory with trivial non-stationarity.Comment: 4 page