Semiclassical treatment of induced schwinger processes at a finite temperature

The induced pair production in an external field at a finite temperature is considered. An one-loop correction to the Green’s function of a meson is calculated semiclassically within the framework of a saddle-point analysis of the Schwinger proper time integrals. This correction appears to be exponentially small in terms of an inverse temperature dependence. The low-temperature limit is shown to be in full agreement with previously obtained zero-temperature results. The corrections in the low-temperature limits are estimated up to the leading exponential and preexponential terms. A comparison is made to earlier calculations of the vacuum decay. The text was submitted by the authors in English.