Rindler solutions and their physical interpretation

We show that the singular behavior of Rindler solutions near horizon testifies to the currents of particles from a region arbitrarily close to the horizon. Besides, the Rindler solutions in right Rindler sector of Minkowski space can be represented as a superposition of only positive-or only negative-frequency plane waves; these states require infinite energy for their creation and possess infinite charge in a finite space interval, containing the horizon. The positive-or negative-frequency representations of Rindler solutions analytically continued to the whole Minkowski space make up a complete set of states in this space, which have, however, the aforementioned singularities. These positive (negative)-frequency states are characterized by positive (negative) total charge, the charge of the same sign in right (left) Rindler sector and by quantum number κ. But in other Lorentz invariant sectors they do not possess positive (negative)-definite charge density and have negative (positive) charge in left (right) Rindler sector. Therefore these states describe both the particle (antiparticle) and pairs, the mean number of which is given by Planck function of κ. These peculiarities make the Rindler set of solutions nonequivalent to the plane wave set and the inference on the existence of thermal currents for a Rindler observer moving in empty Minkowski space is unfounded. Zh. éksp. Teor. Fiz. 114, 777–785 (September 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Classical and quantum scattering by a gravitational center

The corrections to the leading term of the small-angle deflection of a classical particle by the Schwarzschild field and its linear approximation were found. The corresponding cross sections were obtained. The comparison with known in Born approximation cross sections for quantum massless particles of spins 0, 1, and 2 shows that only the leading term in all cases is the same. As the conditions for classical treatment are well fulfilled, this means that the classical results are much more accurate than the quantum one in Born approximation. The fact that the photon cross section is always smaller than that of massless scalar particle (both in Born approximation) suggests that with small probability (at least of order of the difference of these cross sections) the photon can fly by the Sun without deflection. The deflection of light, observable at a final distance from the Sun, is also considered and it is shown that measurements at the distances of several Sun’s radii will decide which coordinate system is the privileged one.     

Gravitational Scattering of a Quantum Particle and the Privileged Coordinate System

In gravitational scattering the quantum particle probes the Fourier-transforms of a metric. I evaluate the Fourier-transforms of Schwarzschildmetrics in standard, harmonic, and other coordinate systems in linear and G²-approximations. In general, different coordinate systems lead to different scattering. This opens up the possibility to choose the privileged coordinate system which should lead to scattering in agreement with experiment.     

Microscopic description of low-energy neutron scattering on a deuteron

Low-energy neutron-deuteron scattering is calculated within the collective adiabatic approach by using a few versions of realistic NN interaction. The resulting integrated cross sections for the process are in good agreement with experimental data.     

Feasibility of experimental investigation of nonlinear QED processes—photon emission by electrons and pair creation by photons in strong laser field

On the basis of the theory of nonlinear QED processes occurring in collisions of high-energy electrons and γ-quanta with a strong laser pulse [1], the feasibility of their experimental investigation is discussed. The use of existing ⋍100 GeV electron beam accelerators and terawatt lasers of ultrashort pulses enables one to attain optimal values for the parameters and to have fields ⋍F_o=m²c³/ħe act on the electron. The choice and organization of laser system, synchronization of accelerator and laser operation, distributions of created γ-quanta and e⁺e⁻-pairs in different variables and parameters, their dependence on polarization of laser target and incident particles, background problems, and other questions connected with carrying out the experiments are discussed. Translated from preprint No. 11, 1993 of the Lebedev Physics Institute, Moscow, Russia.     

Stokes line width

The concept of Stokes line width is introduced for the asymptotic expansions of functions near an essential singularity. Explicit expressions are found for functions (switching functions) that switch on the exponentially small terms for the Dawson integral, Airy function, and the gamma function. A different, more natural representation of a function, not associated with expansion in an asymptotic series, in the form of dominant and recessive terms is obtained by a special division of the contour integral which represents the function into contributions of higher and lower saddle points. This division leads to a narrower, natural Stokes line width and a switching function of an argument that depends on the topology of the lines of steepest descent from the saddle point.P. N. Lebedev Physics Institute, Rossiskoi Adademii Nauk. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 1, pp. 24–40, July, 1992.     

The vacuum-vacuum amplitude and Bogoliubov coefficients

We consider the problem of fixing the phases of Bogoliubov coefficients in quantum electrodynamics such that the vacuum-vacuum amplitude can be expressed via them. For a constant electric field and particles with spins of 0 and 1/2, this is done starting from the definition of these coefficients. Using the symmetry etween electric and magnetic fields, we extend the result to a constant electromagnetic field. It turns out that for a constant magnetic field, it is necessary to distinguish the in-and out-states, although they differ only by a phase factor. For a spin-1 particle with a gyromagnetic of ratio g=2, this approach fails and we reconsider the problem using the proper-time method.     

Classical and quantum scattering by a Coulomb potential

For relativistic energies the small-angle classical cross section for scattering on a Coulomb potential agrees with the first Born approximation for quantum cross section for scalar particle only in the leading term. The disagreement in other terms can be avoided if the sum of all corrections to the first Born approximation for large enough Coulomb charge contains the classical terms which are independent of that charge. The difference in classical and quantum cross sections may be partly attributed to the fact that the relativistic quantum particle can rush through the field without interaction. We expect that smaller impact parameters and spin facilitate this effect. The text was submitted by the authors in English.     

Gravitation according to theory of sources

The metric of spherically symmetric ball of ideal incompressible liquid is considered in G²-approximation with the help of the theory of sources. Using the integral equations of this theory gives the exterior metric depending upon the radius b of the ball of matter in some terms proportional to G².