8,497 research outputs found
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.
Quadratic perturbations of quadratic codimension-four centers
We study the stratum in the set of all quadratic differential systems
with a center, known as the
codimension-four case . It has a center and a node and a rational first
integral. The limit cycles under small quadratic perturbations in the system
are determined by the zeros of the first Poincar\'e-Pontryagin-Melnikov
integral . We show that the orbits of the unperturbed system are elliptic
curves, and is a complete elliptic integral. Then using Picard-Fuchs
equations and the Petrov's method (based on the argument principle), we set an
upper bound of eight for the number of limit cycles produced from the period
annulus around the center
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
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