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

Abstract

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 $\beta_{12}$ 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 $w_0/2\pi$ 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 $\alpha^{B,F}$ 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 $\alpha_0=1/4\pi$ for fine structure constant are the bare, nonrenormalized values.