| Summary: | The instability of electron-positron vacuum in strong electric fields is studied. First, falling to the Coulomb center is discussed at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Z</mi><mo>></mo><mn>137</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> for a spinless boson and at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Z</mi><mo>></mo><mn>137</mn></mrow></semantics></math></inline-formula> for electron. Subsequently, focus is concentrated on description of deep electron levels and spontaneous positron production in the field of a finite-size nucleus with the charge <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Z</mi><mo>></mo><msub><mi>Z</mi><mi>cr</mi></msub><mo>≃</mo><mn>170</mn></mrow></semantics></math></inline-formula>. Next, these effects are studied in application to the low-energy heavy-ion collisions. Subsequently, we consider phenomenon of “electron condensation” on levels of upper continuum crossed the boundary of the lower continuum <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><mo>=</mo><mo>−</mo><mi>m</mi></mrow></semantics></math></inline-formula> in the field of a supercharged nucleus with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Z</mi><mo>≫</mo><msub><mi>Z</mi><mi>cr</mi></msub></mrow></semantics></math></inline-formula>. Finally, attention is focused on many-particle problems of polarization of the quantum electrodynamics (QED) vacuum and electron condensation at ultra-short distances from a source of charge. We argue for a principal difference of cases, when the size of the source is larger than the pole size <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mi>pole</mi></msub></semantics></math></inline-formula>, at which the dielectric permittivity of the vacuum reaches zero and smaller <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mi>pole</mi></msub></semantics></math></inline-formula>. Some arguments are presented in favor of the logical consistency of QED. All of the problems are considered within the same relativistic semiclassical approach.
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