arXiv subjects

A. I. Nikishov

Publications and source records attributed to A. I. Nikishov.

23 records · Page 2Linked to original sources

arXiv2002

Equivalent sets of solutions of the Klein-Gordon equation with a constant electric field

In connection with the problem of choosing the in- and out-states among the solutions of a wave equation with one-dimensional potential we study nonstationary and "stationary" families of complete sets. A nonstationary set consists of the solutions with the quantum number $p_v=p^0v-p_3.$ It can be obtained from the nonstationary set with quantum number $p_3$ by a boost along $x_3$-axis (along the direction of the electric field) with velocity $-v$. By changing the gauge the solutions in all sets can be brought to one and the same potential without changing quantum numbers. Then the transformations of solutions of one set (with quantum number $p_v$) to the solutions in another set (with quantum number $p_{v'}$) have the group properties. The "stationary" solutions and sets possess the same properties as the nonstationary ones and are obtainable from stationary solutions with quantum number $p^0$ by the same boost. It turns out that any set can be obtained from any other by gauge manipulations. So all sets are equivalent and the classification (i.e. ascribing the frequency sign and in-, out- indexes) in any set is determined by the classification in $p_3$-set, where it is evident.

hep-ph↗

arXiv2001

Vector boson in constant electromagnetic field

The propagator and complete sets of in- and out-solutions of wave equation, together with Bogoliubov coefficients, relating these solutions, are obtained for vector $W$-boson (with gyromagnetic ratio $g=2$) in a constant electromagnetic field. When only electric field is present the Bogoliubov coefficients are independent of boson polarization and are the same as for scalar boson. When both electric and magnetic fields are present and collinear, the Bogoliubov coefficients for states with boson spin perpendicular to the field are again the same as in scalar case. For $W^-$ spin along (against) the magnetic field the Bogoliubov coefficients and the contributions to the imaginary part of the Lagrange function in one loop approximation are obtained from corresponding expressions for scalar case by substitution $m^2\to m^2+2eH$ $(m^2\to m^2-2eH)$. For gyromagnetic ratio $g=2$ the vector boson interaction with constant electromagnetic field is described by the functions, which can be expected by comparing wave functions for scalar and Dirac particle in constant electromagnetic field.

hep-th↗

arXiv2000

Weinberg's energy-momentum pseudotensor for Schwarzschild field

Weinberg's energy-momentum pseudotensor is obtained for Schwarzschild metric in harmonic coordinates. On the horizon it possesses unintegrable singularities. For this reason the total energy of a collapsar can't be obtained by integrating energy density over the system's volume. The implication for gravity theories is noted. A thought on how to choose unique energy-momentum tensor is given.

gr-qc↗

arXiv1999

On energy-momentum tensors of gravitational field

Several energy-momentum "tensors" of gravitational field are considered and compared in the lowest approximation. Each of them together with energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from the other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Starting from Lorentz invariance the Lagrangians for spin-2, mass-0 field are considered. They differ only by divergences. From these Lagrangians by Belinfante-Rosenfeld procedure the energy-momentum tensors are build. Using each of these tensors in 3-graviton vertex we obtain the corresponding metric of a Newtonian center in $G^2$ approximation. Only one of these ''field-theretical''tensors (namely the half sum of Thirring tensor and tensor obtained from Lagrangian given by Misner, Thorne and Wheeler) leads to correct value of the perihelion shift. This tensor does not coincide with Weinberg`s one (directly obtainable from Einstein equation) and gives metric of a spherical body differing (in space part of metric in the first nonlinear approximation) from Schwarzschild field in harmonic coordinates. As a result a relativistic particle in such field must move note according general relativity prescriptions. This approach puts the gravitational energy-momentum tensor on the same footing as any other energy-momentum tensor.

gr-qc↗

arXiv1999

On an Alternative Approach to Gravitation

Several energy-momentum "tensors" of gravitational field are considered and compared in the lowest approximation. Each of them together with energy-momentum tensor of point-like particles satisfies the conservation laws when equation of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from the other in the way their energy density is distributed between energy density of interection (nonzero only at locations of particles) and energy density of gravitational field. Starting from Lorentz invariance the Lagrangians for spin-2, mass-0 field are constracted. They differ only by divergences. From these Lagrangians by Belinfante-Rosenfeld procedure the energy-momentum tensors are build. Only one of them is suitable for explaining the perihelion shift. This tensor does not coincide with Weinberg`s one (directly obtainable from Einstein equation). It is noted that phenomenological field-theoretical approach (utilizing only vertices and propagators) can lead to modification of theory in the region of strong field, where till now no observational data are available.

hep-th↗