85 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.
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
On Quantization of Time-Dependent Systems with Constraints
The Dirac method of canonical quantization of theories with second class
constraints has to be modified if the constraints depend on time explicitly. A
solution of the problem was given by Gitman and Tyutin. In the present work we
propose an independent way to derive the rules of quantization for these
systems, starting from physical equivalent theory with trivial
non-stationarity.Comment: 4 page
Quantization of (2+1)-spinning particles and bifermionic constraint problem
This work is a natural continuation of our recent study in quantizing
relativistic particles. There it was demonstrated that, by applying a
consistent quantization scheme to a classical model of a spinless relativistic
particle as well as to the Berezin-Marinov model of 3+1 Dirac particle, it is
possible to obtain a consistent relativistic quantum mechanics of such
particles. In the present article we apply a similar approach to the problem of
quantizing the massive 2+1 Dirac particle. However, we stress that such a
problem differs in a nontrivial way from the one in 3+1 dimensions. The point
is that in 2+1 dimensions each spin polarization describes different fermion
species. Technically this fact manifests itself through the presence of a
bifermionic constant and of a bifermionic first-class constraint. In
particular, this constraint does not admit a conjugate gauge condition at the
classical level. The quantization problem in 2+1 dimensions is also interesting
from the physical viewpoint (e.g. anyons). In order to quantize the model, we
first derive a classical formulation in an effective phase space, restricted by
constraints and gauges. Then the condition of preservation of the classical
symmetries allows us to realize the operator algebra in an unambiguous way and
construct an appropriate Hilbert space. The physical sector of the constructed
quantum mechanics contains spin-1/2 particles and antiparticles without an
infinite number of negative-energy levels, and exactly reproduces the
one-particle sector of the 2+1 quantum theory of a spinor field.Comment: LaTex, 24 pages, no figure
Creation of Dirac neutrinos in a dense medium with time-dependent effective potential
We consider Dirac neutrinos interacting with background fermions in the frame
of the standard model. We demonstrate that a time-dependent effective potential
is quite possible in a protoneutron star (PNS) at certain stages of its
evolution. For the first time, we formulate a nonperturbative treatment of
neutrino processes in a matter with arbitrary time-dependent effective
potential. Using linearly growing effective potential, we study the typical
case of a slowly varying matter interaction potential. We calculate
differential mean numbers of pairs created from the vacuum by
this potential and find that they crucially depend on the magnitude of masses
of the lightest neutrino eigenstate. These distributions uniformly span up to
eV energies for muon and tau neutrinos created in PNS core due to the
compression just before the hydrodynamic bounce and up to eV
energies for all three active neutrino flavors created in the neutronization.
Considering different stages of the PNS evolution, we derive constraints on
neutrino masses, eV corresponding to the
nonvanishing pairs flux produced by this mechanism. We show
that one can distinguish such coherent flux from chaotic fluxes of any other
origin. Part of these neutrinos, depending on the flavor and helicity, are
bounded in the PNS, while antineutrinos of any flavor escape the PNS. If the
created pairs are , then a part of the corresponding
neutrinos also escape the PNS. The detection of and with
such low energies is beyond current experimental techniques.Comment: 18 pages, Revtex4.1, 1 eps figure, 2 columns; minimal changes,
version to be published in Phys. Rev.
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