The interacting system of electrons, positrons and photons in high external electric and arbitrary magnetic fields

Abstract

The connected system of Boltzman equations for the interacting system of electrons, positrons and photons in high external electric E and arbitrary magnetic H fields is solved. The consideration is made under the conditions of arbitrary heating and the mutual drag of carriers and photons. The non-stationary and non-uniform distribution function (DF) of photons for the all considered cases is obtained. It is shown that the DF of photons have the stationary limit for the drift velocities $(\overset{\to }\to{u}\overset{\to}\to{q}/\hbar ω_q) <1$ and becomes exponentially grown by the time for the drift velocities $(\overset{\to}\to{u}\overset{\to}\to{q}/\hbar ω_q) \geq 1$. It is shown that the mutual drag of carriers and photons leads to the formation of ''quasi-particles''\_ the ''electron dressed by photons'' and ''positron dressed by photons'', i.e. the mutual drag plays the role of the dressing mechanism of carriers and leads to the renormalization of the mass and frequency of photons. As a result of analyses of the phenomena of connected by the mutual drag system of carriers and photons we receive some fundamental results: a) the finiteness of the mass of photon (i.e. the rest mass of photons do not equal to zero); b) reality of takhyons as a quasi-particles with the real mass in amplifying system (or regime); c) identity of the mechanism of relativity and the Doppler effect which coincides with the renormalization of frequency or mass as a result of the mutual drag of carriers and photons at external field (force). These conclusions were received as a result of the fact that the relativistic factor enters to the expressions of the DF of photons and other physical expressions in the first order in the form $[ 1-(u^2/c^2) ] ^{-1}$, instead the $[ 1-(u^2/c^2) ] ^{-1/2}$ in Einstein theory. It is shown that the relativistic effect of deceleration of time really taking place for the relaxation time of carriers or for the life time of carriers, or for the period of electromagnetic oscillations. The latest is a direct result of the Doppler effect. Also it is shown that the velocity of light is an averaged velocity of photons at the ground state, as well as a velocity of sound for the phonons.