7,128 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
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
Quantum scalar field in FRW Universe with constant electromagnetic background
We discuss massive scalar field with conformal coupling in
Friedmann-Robertson-Walker (FRW) Universe of special type with constant
electromagnetic field. Treating an external gravitational-electromagnetic
background exactly, at first time the proper-time representations for out-in,
in-in, and out-out scalar Green functions are explicitly constructed as
proper-time integrals over the corresponding (complex) contours. The
vacuum-to-vacuum transition amplitudes and number of created particles are
found and vacuum instability is discussed. The mean values of the current and
energy-momentum tensor are evaluated, and different approximations for them are
investigated. The back reaction of the particles created to the electromagnetic
field is estimated in different regimes. The connection between proper-time
method and effective action is outlined. The effective action in scalar QED in
weakly-curved FRW Universe (De Sitter space) with weak constant electromagnetic
field is found as derivative expansion over curvature and electromagnetic field
strength. Possible further applications of the results are briefly mentioned.Comment: 38 pages, LaTe
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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