Vladimir I. Ritus

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

We consider the symmetry between creation of pairs of massless bosons or fermions by an accelerated mirror in (1+1)-dimensional space and emission of single photons or scalar quanta by an electric or scalar charge in (3+1)-dimensional space. The relation of Bogoliubov coefficients describing the processes generated by a mirror to Fourier components of the current or charge density implies that the spin of any disturbances bilinear in the scalar or spinor field coincides 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 to invariant singular solutions and the Green functions of wave equations for both (1+1)-and (3+1)-dimensional spaces, and especially for the integral relations between these solutions. One of these relations leads to the coincidence of the self-action changes and vacuum-vacuum amplitudes for an accelerated mirror in two-dimensional space-time and a charge in four-dimensional space-time. Both invariants of the Lorentz group, spin and mass, play an essential role in the established symmetry. The symmetry embraces not only the processes of real quanta radiation, but also the processes of the mirror and charge interactions with fields carrying spacelike momenta. These fields accompany their sources and determine the Bogoliubov matrix coefficients αω′ωB, F. It is shown that the Lorentz-invariant traces ±trαB,F describe the vector and scalar interactions of the accelerated mirror with a uniformly moving detector. This interpretation rests essentially on the relation between propagators of the waves with spacelike momenta in two-and four-dimensional spaces. The traces ±trαB, F coincide with the products of the mass shift Δm1, 0 of the accelerated electric or scalar charge and the proper time of the shift formation. The symmetry fixes the value of the bare fine structure constant α0=1/4π.

A symmetry relating certain processes in 2- and 4-dimensional space-times and the value α0 = 1/4π of 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

Rindler solutions and their physical interpretation

e^2/ \hbar c

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

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

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

e=\sqrt{\hbar c}

Physical properties of scalar and spinor field states with the Rindler-Milne (hyperbolic) symmetry

. 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

The doubling of the anomalous magnetic moment of electron in a very strong constant homogeneous electric field

\beta_{12}

Problems of theoretical physics

of the ends and maximum proper acceleration

Lagrangian of an intense electromagnetic field and quantum electrodynamics at short distances

w_0

Shift and Splitting of Atomic Energy Levels by the Field of an Electromagnetic Wave

are expressed in terms of heat capacity (or energy) spectral densities of Bose and Fermi massless particle gases with temperature