8,099 research outputs found
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
Arbitrarily slow, non-quasistatic, isothermal transformations
For an overdamped colloidal particle diffusing in a fluid in a controllable,
virtual potential, we show that arbitrarily slow transformations, produced by
smooth deformations of a double-well potential, need not be reversible. The
arbitrarily slow transformations do need to be fast compared to the barrier
crossing time, but that time can be extremely long. We consider two types of
cyclic, isothermal transformations of a double-well potential. Both start and
end in the same equilibrium state, and both use the same basic operations---but
in different order. By measuring the work for finite cycle times and
extrapolating to infinite times, we found that one transformation required no
work, while the other required a finite amount of work, no matter how slowly it
was carried out. The difference traces back to the observation that when time
is reversed, the two protocols have different outcomes, when carried out
arbitrarily slowly. A recently derived formula relating work production to the
relative entropy of forward and backward path probabilities predicts the
observed work average.Comment: 6 pages, 6 figure
Dirac equation in the magnetic-solenoid field
We consider the Dirac equation in the magnetic-solenoid field (the field of a
solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm
solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using
von Neumann's theory of deficiency indices. We find self-adjoint extensions of
the Dirac Hamiltonian in both above dimensions and boundary conditions at the
AB solenoid. Besides, for the first time, solutions of the Dirac equation in
the magnetic-solenoid field with a finite radius solenoid were found. We study
the structure of these solutions and their dependence on the behavior of the
magnetic field inside the solenoid. Then we exploit the latter solutions to
specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm
solenoid.Comment: 23 pages, 2 figures, LaTex fil
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
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
Coherent states of non-relativistic electron in magnetic-solenoid field
We construct coherent states of a nonrelativistic electron in the
magnetic-solenoid field, which is a superposition of the Aharonov-Bohm field
and a collinear uniform magnetic field. In the problem under consideration
there are two kind of coherent states, the first kind corresponds to classical
trajectories which embrace the solenoid and the second one to trajectories
which do not. Mean coordinates in the constructed coherent states are moving
along classical trajectories, the coherent states maintain their form under the
time evolution, and represent a complete set of functions, which can be useful
in semi classical calculations. In the absence of the Aharonov-Bohm filed these
states are reduced to the well-known in the case of uniform magnetic field
Malkin-Man'ko coherent states.Comment: 11 pages, version accepted for publication in J. Phys. A, 3 figures
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Quantum spinor field in the FRW universe with a constant electromagnetic background
The article is a natural continuation of our paper {\em Quantum scalar field
in FRW Universe with constant electromagnetic background}, Int. J. Mod. Phys.
{\bf A12}, 4837 (1997). We generalize the latter consideration to the case of
massive spinor field, which is placed in FRW Universe of special type with a
constant electromagnetic field. To this end special sets of exact solutions of
Dirac equation in the background under consideration are constructed and
classified. Using these solutions representations for out-in, in-in, and
out-out spinor Green functions are explicitly constructed as proper-time
integrals over the corresponding contours in complex proper-time plane. The
vacuum-to-vacuum transition amplitude 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
presented. The back reaction related to particle creation and to the
polarization of the unstable vacuum is estimated in different regimes.Comment: 36 pages, LaTex fil
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