7,126 research outputs found
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
QED in external field with space-time uniform invariants: Exact solutions
We study exact solutions of Dirac and Klein-Gordon equations and Green functions in d-dimensional QED and in an external electromagnetic field with constant and homogeneous field invariants. The cases of even and odd dimensions are considered separately, they are essentially different. We direct attention to the asymmetry of the quasienergy spectrum, which appears in odd dimensions. The in and out classification of the exact solutions as well as the completeness and orthogonality relations is strictly proven. Different Green functions in the form of sums over the exact solutions are constructed. The Fock-Schwinger proper time integral representations of these Green functions are found. As physical applications we consider the calculations of different quantum effects related to the vacuum instability in the external field. For example, we present mean values of particles created from the vacuum, the probability of the vacuum remaining a vacuum, the effective action, and the expectation values of the current and energy-momentum tensor
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