arXiv subjects

V. I. Ritus

Publications and source records attributed to V. I. Ritus.

6 recordsLinked to original sources

arXiv2005

The symmetry, connecting the processes in 2- and 4-dimensional space-times, and the value $α_0 = 1/4π$ for the bare fine structure constant

Defined by Bogoliubov coefficients the spectra of pairs of Bose (Fermi) massless quanta, emitted by point mirror in 1+1-space, coincide up to multiplier $e^2/ \hbar c$ with the spectra of photons (scalar quanta), emitted by point electric (scalar) charge in 3+1-space for any common trajectory of the sources. The integral connection of the propagator of a pair in 1+1-space with the propagator of a single particle in 3+1-space leads to equality of the vacuum-vacuum amplitudes for charge and mirror if the mean number of created particles is small and the charge $e=\sqrt{\hbar c}$. Due to the symmetry the mass shifts of electric and scalar charges, the sources of Bose-fields with spin 1 and 0 in 3+1-space, for the trajectories with subluminal relative velocity $β_{12}$ of the ends and maximum proper acceleration $w_0$ are expressed in terms of heat capacity (or energy) spectral densities of Bose and Fermi massless particle gases with temperature $w_0/2π$ in 1+1-space. The energy of one-dimensional proper field oscillations is partly deexcited in the form of real quanta and partly remains in the field. As a result, the mass shift of accelerated electric charge is nonzero and negative, while that of scalar charge is zero. The traces of the Bogoliubov coefficients $α^{B,F}$ describe the vector and scalar interactions of accelerated mirror with a uniformly moving detector and were found in analytical form. The symmetry predicts one and the same value $e_0=\sqrt{\hbar c}$ for electric and scalar charges in 3+1-space. The arguments are adduced in favour of that this value and the corresponding value $α_0=1/4π$ for fine structure constant are the bare, nonrenormalized values.

hep-th↗

arXiv2005

Asymptotic representations for some functions and integrals connected with the Airy function

The asymptotic representations of the functions ${\rm Ai}_1(x), {\rm Gi}(x), {\rm Ai}'(x), {\rm Ai}^2(x), {\rm Bi}^ 2(x)$ are obtained. As a by-product, the factorial identity (21') is found. The derivation of asymptotic representations of the integral $\int_v^{\infty}dx{\rm Ai}(x)h(x,v)$ for $v\to-\infty$ and integrals, differing from it by the change of ${\rm Ai}(x)$ by ${\rm Ai}'(x)$ or ${\rm Ai_1(x)}$, is presented. For the Airy function ${\rm Ai}(z)$, as an example, the Stokes' phenomenon is considered as a consequence of discontinuous behavior of steepest descent lines over the passes. When $z$ crosses the Stokes ray, the steepest descent line over the higher pass abruptly changes the direction of its asymptotic approach to the steepest descent line over the lower pass to the direction of approach to the opposite end of this line. Therefore, when the integration contour, drawn along the steepest descent lines, goes over the higher pass, it begins or stops to go over the lower pass while $z$ crosses the Stokes ray, and as a result the recessive series (contribution from the lower pass) discontinuously appears or disappears in the asymptotic representation of a function containing the dominant series.

math-ph↗

arXiv2003

The symmetry, inferable from Bogoliubov transformation, between the processes induced by the mirror in two-dimentional and the charge in four-dimentional space-time

The symmetry between the creation of pairs of massless bosons or fermions by accelerated mirror in 1+1 space and the emission of single photons or scalar quanta by electric or scalar charge in 3+1 space is deepened in this paper. The relation of Bogoliubov coefficients with Fourier's components of current or charge density leads to the coicidence of the spin of any disturbances bilinear in scalar or spinor field with the spin of quanta emitted by the electric or scalar charge. The mass and invariant momentum transfer of these disturbances are essential for the relation of Bogoliubov coefficients with Green's functions of wave equations both for 1+1 and 3+1 spaces. Namely the relation (20) leads to the coincidence of the self-action changes and vacuum-vacuum amplitudes for the accelerated mirror in 1+1 space and charge in 3+1 space. Thus, both invariants of the Lorentz group, spin and mass, perform intrinsic role in established symmetry. The symmetry embraces not only the processes of real quanta radiation. It extends also to the processes of the mirror and the charge interactions with the fields carring spacelike momenta. These fields accompany their sources and define the Bogoliubov matrix coefficients α^{B,F}. It is shown that the traces of α^{B,F} describe the vector and scalar interactions of accelerated mirror with uniformly moving detector. This interpretation rests essentially on the relation (100) between the propagators of the waves with spacelike momenta in 2- and 4-dimentional spaces. The traces of α^{B,F} coincide actually with the products of the mass shift Δm_{1,0} of accelerated electric or scalar charge and the proper time of the shift formation. The symmetry fixes the value of the bare fine structure constant α_0=1/4π.

hep-th↗

arXiv1999

Common vacuum conservation amplitude in the theory of the radiation of mirrors in two-dimensional space-time and of charges in four-dimensional space-time

The action changes (and thus the vacuum conservation amplitudes) in the proper-time representation are found for an accelerated mirror interacting with scalar and spinor vacuum fields in 1+1 space. They are shown to coincide to within the multiplier e^2 with the action changes of electric and scalar charges accelerated in 3+1 space. This coincidence is attributed to the fact that the Bose and Fermi pairs emitted by a mirror have the same spins 1 and 0 as do the photons and scalar quanta emitted by charges. It is shown that the propagation of virtual pairs in 1+1 space can be described by the causal Green's function Δ_f(z,μ) of the wave equation for 3+1 space. This is because the pairs can have any positive mass and their propagation function is represented by an integral of the causal propagation function of a massive particle in 1+1 space over mass which coincides with Δ_f(z,μ). In this integral the lower limit μis chosen small, but nonzero, to eliminate the infrared divergence. It is shown that the real and imaginary parts of the action change are related by dispersion relations, in which a mass parameter serves as the dispersion variable. They are a consequence of the same relations for Δ_f(z,μ). Therefore, the appearance of the real part of the action change is a direct consequence of the causality, according to which real part of Δ_f(z,μ) is nonzero only for timelike and zero intervals.

hep-th↗

arXiv1999

Symmetries and causes of the coincidence of the radiation spectra of mirrors and charges in 1+1 and 3+1 spaces

This paper discusses the symmetry of the wave field that lies to the right and left of a two-sided accelerated mirror in 1 + 1 space and satisfies a single condition on it. The symmetry is accumulated in the Bogolyubov matrix coefficients $α$ and $β$ that connect the two complete sets of solutions of the wave equations. The amplitudes of the quantum processes in the right and left half-spaces are expressed in terms of $α$ and $β$ and are related to each other by transformation (12). Coefficient $β_{ω'ω}^*$ plays the role of the source amplitude of a pair of particles that are directed to opposite sides with frequencies $ω$ and $ω'$ but that are in either the left or the right half-space as a consequence of the reflection of one of them. Such an interpretation makes $β_{ω'ω}^*$ observable and explains the equalities, given by Eq. (1) and found earlier by Nikishov and author [Zh. Eksp. Teor. Fiz. 108, 1121 (1995)] and by author [Zh. Eksp. Teor. Fiz. 110, 526 (1996)] that the radiation spectra of a mirror in 1+1 space coincide with those of charges in 3 + 1 space by the fact that the moment of the pair emitted by the mirror coincide with the spin of the single particle emitted by the charge.

hep-th↗

arXiv1998

Effective Lagrange function of intense electromagnetic field in QED

The short survey of computation and properties of effective Lagrange function of intensive field in two-loop approximation accounting for radiative interaction of virtual electrons is given. The renormalization of field, charge and mass is completely defined by the weak field behaviour of the exact Lagrange function: its real part must be Maxwellian and imaginary part must be quasiclassical $\propto \exp (-πm^2c^3/\hbar eε)$. For weak electric field radiative interaction manifests itself as electron mass shift. Using the renorminvariance at strong field and exponentiation at weak field it is possible to obtain information about contributions of high order in $α$.

hep-th↗