All the results reffering to the relations of the optical theorem in QED with an external electromagnetic field with unstable vacuum are consistently given in this paper. The results obtained are true in all orders of perturbation theory. A generating functional is introduced for calculating total probabilities of any processes in QED with unstable vacuum.

No abstract

We study particles creation in arbitrary space-time dimensions by external electric fields, in particular, by fields, which are acting for a finite time. The time and dimensional analysis of the vacuum instability is presented. It is shown that the distributions of particles created by quasiconstant electric fields can be written in a form which has a thermal character and seems to be universal. Its application, for example, to the particles creation in external constant gravitational field reproduces the Hawking temperature exactly.Comment: 36 pages, LaTe

We adopt the Dirac model for graphene and calculate the Casimir interaction energy between a plane suspended graphene sample and a parallel plane perfect conductor. This is done in two ways. First, we use the quantum-field-theory approach and evaluate the leading-order diagram in a theory with 2 + 1-dimensional fermions interacting with 3 + 1-dimensional photons. Next, we consider an effective theory for the electromagnetic field with matching conditions induced by quantum quasiparticles in graphene. The first approach turns out to be the leading order in the coupling constant of the second one. The Casimir interaction for this system appears to be rather weak. It exhibits a strong dependence on the mass of the quasiparticles in graphene.

QED with strong external backgrounds that can create particles from the vacuum is well developed for the so-called t-electric potential steps, which are time-dependent external electric fields that are switched on and off at some time instants. However, there exist many physically interesting situations where external backgrounds do not switch off at the time infinity. E.g., these are timeindependent nonuniform electric fields that are concentrated in restricted space areas. The latter backgrounds represent a kind of spatial x-electric potential steps for charged particles. They can also create particles from the vacuum, the Klein paradox being closely related to this process. Approaches elaborated for treating quantum effects in the t-electric potential steps are not directly applicable to the x-electric potential steps and their generalization for x-electric potential steps was not sufficiently developed. We believe that the present work represents a consistent solution of the latter problem. We have considered a canonical quantization of the Dirac and scalar fields with x-electric potential step and have found in-and out-creation and annihilation operators that allow one to have particle interpretation of the physical system under consideration. To identify in-and out-operators we have performed a detailed mathematical and physical analysis of solutions of the relativistic wave equations with an x-electric potential step with subsequent QFT analysis of correctness of such an identification. We elaborated a nonperturbative (in the external field) technique that allows one to calculate all characteristics of zero-order processes, such, for example, scattering, reflection, and electron-positron pair creation, without radiation corrections, and also to calculate Feynman diagrams that describe all characteristics of processes with interaction between the in-, out-particles and photons. These diagrams have formally the usual form, but contain special propagators. Expressions for these propagators in terms of in-and out-solutions are presented. We apply the elaborated approach to two popular exactly solvable cases of x-electric potential steps, namely, to the Sauter potential and to the Klein step.