12,252 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.
On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields
We prove that every heteroclinic saddle loop (a two-saddle cycle) occurring
in an analytic finite-parameter family of plane analytic vector fields, may
generate no more than a finite number of limit cycles within the family.Comment: 21 pages, 10 figures, a new section explaining the so called "Petrov
trick" in the context of the paper is added. The paper will appear in
"Functional Analysis and Its Applications" (2013
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