The instability of electron-positron vacuum in strong electric fields is studied. First, falling to the Coulomb center is discussed at $Z>137/2$ for a spinless boson and at $Z>137$ 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 $Z>Z_{\mathrm{cr}}\simeq 170$. 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 $ϵ=-m$ in the field of a supercharged nucleus with $Z\gg Z_{\mathrm{cr}}$. 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 $r_{\mathrm{pole}}$, at which the dielectric permittivity of the vacuum reaches zero and smaller $r_{\mathrm{pole}}$. Some arguments are presented in favor of the logical consistency of QED. All of the problems are considered within the same relativistic semiclassical approach.

We consider the model of composite dark matter assuming stable particles of charge $-2$ bound with primordial He nuclei by the Coulomb force in $O\mathrm{He}$ atoms. We study the capture of such dark atoms in matter and propose the possibility of the existence of stable $O$-enriched superheavy nuclei and $O$ nuclearites, in which heavy $O$ dark matter fermions are bound by electromagnetic forces with ordinary nuclear matter. $O\mathrm{He}$ atoms accumulation in stars and its possible effect on stellar evolution is also considered, extending the set of indirect probes for composite dark matter.

$S$-wave pion-nucleon interactions in the linear sigma model, and in Manohar-Georgi and Gasser-Sainio-Svarc models with finite number of terms in Lagrangians, as well as in a general phenomenological approach are reviewed. Subtleties associated with the current algebra theorems and field redefinitions are discussed. In the first and third models most likely the $s$-wave pion condensation in the isospin-symmetric matter does not occur at least up to high densities, whereas within the second model it may appear already at moderate densities. In the phenomenological approach two parametrizations of the $s$-wave pion-nucleon scattering amplitude and the pion polarization operator used in the literature are considered. The first parametrization employs the off-mass-shell amplitude and allows to fulfil the current algebra theorems. Using it the $s$-wave pion polarization operator in the isospin-symmetric matter is reconstructed within the gas approximation. With this pion polarization operator the $s$-wave pion condensation in the isospin-symmetric matter does not occur at least up to high densities. Second parametrization uses the on-mass-shell pion-nucleon scattering amplitude and does not satisfy the Adler and Weinberg conditions. With such a parametrization most likely the $s$-wave pion condensation in the isospin-symmetric matter may occur already at the nucleon density $n\simeq (1.4-2.5)n_0$, where $n_0$ is the density of the atomic nucleus, that should result in observable effects. Both parametrizations allow us to successfully describe the pion atom data.

Instability of the charged pion vacuum resulting in the pion condensation is studied within the λ | ϕ | 4 model at the rapid rotation of the system in presence of external fields. Case of the static external scalar and electric square potential wells and the uniform magnetic field is studied in detail. The Meissner and Aharonov-Bohm effects and the London moment are taken into account. Analogies and differences with the behavior of metallic superconductors under the action of the rotation and the external magnetic field are analyzed. Published by the American Physical Society 2025

Possibilities of the formation of the pion-sigma meson field vortices in a rotating empty vessel (in vacuum) and in the pion-sigma Bose-Einstein condensates at a dynamically fixed particle number are studied within the linear $\sigma$ model at zero temperature. The charged $\sigma {\pi }^{\pm }$ and neutral $\sigma {\pi }^0$ complex field Ansätze (models 1 and 2) are studied. First it is analyzed which of these configurations is energetically favorable in case of the system at rest. Then conditions are found at which a chiral field storm can arise in a rotating empty vessel. In model 1, an important role played by the electric field is demonstrated. Its appearance may allow for formation of a supervortex (vortex with a large angular momentum) in case of the empty vessel rotating with an overcritical angular velocity. Influence of magnetic field is also studied. Field configurations in presence and absence of the meson self-interaction are found in both models. Then it is shown that the description of the charged (in model 1) and neutral (in model 2) rotating pion-sigma Bose-Einstein condensates is analogous to that for the Bose-Einstein condensates in cold atomic gases. Various field configurations such as vortex lines, rings and spirals are discussed. Conditions for existence of the rigid-body rotation of the vortex lattice are then analyzed. Observational effects for vortex fields in rotating vessels, energetic heavy-ion collisions and in rotating superheavy nuclei and nuclearites are discussed.