Spontaneous emission in the supercritical QED: What is wrong and what is possible

Abstract

Spontaneous positron emission, caused by the supercritical Coulomb source with charge [Formula: see text] and size [Formula: see text], is explored in essentially nonperturbative approach with emphasis on the VP-energy [Formula: see text] a , considered as a function of the Coulomb source parameters [Formula: see text] and [Formula: see text]. The specific contribution to [Formula: see text], which appears in the supercritical case due to direct Coulomb interaction between VP-charge densities [Formula: see text], is outlined and studied in detail. It is shown that after first levels diving into the lower continuum, this contribution to [Formula: see text], being properly renormalized, turns out to be negative in contrast to the classical electrostatics and so could play an important role in spontaneous emission, especially for [Formula: see text] just above the first [Formula: see text]. The additional problems of spontaneous emission, caused by the lepton number conservation, are also discussed.