Abstract
The Gerstein–Greiner–Zeldovich effect—the spontaneous emission of vacuum positrons under conditions of Coulomb supercriticality—has been studied in detail based on the first principles of quantum electrodynamics within the framework of an essentially nonperturbative approach based on a special combination of analytical methods, computer algebra, and numerical calculations. Particular attention is paid to the vacuum energy ({kern 1pt} {{mathcal{E}}_{{{text{VP}}}}}), considered a function of the parameters of the external Coulomb source: charge (Z) and radius (R). The specific contribution to ({kern 1pt} {{mathcal{E}}_{{{text{VP}}}}}) arising due to the direct Coulomb interaction of the vacuum charge densities ({{varrho }_{{{text{VP}}}}}(vec {r})) has been studied in detail. It is shown that, with correct renormalization, this contribution becomes negative after the first discrete levels descend into the lower continuum. Therefore, it is a purely quantum effect, not observed in classical electrodynamics. The problem of lepton number conservation during spontaneous emission is also discussed.