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Topological lumps are known to be present in gluonic fields of SU(3) gluodynamics. Near the transition temperature they were classified either as constituents of nondissociated (anti)calorons, or as constituents of (anti)dyon pairs, or as isolated (anti)dyons. In this paper we study the density and correlation functions of these objects at temperature T/T_c=0.96., Comment: 5 pages, 1 figure. arXiv admin note: text overlap with arXiv:1309.7850

The paper considers the problem of non-visual data recovery from images acquired by land-survey satellites. Such non-visual data include: dynamics and parameters of land-survey satellite angular motion along an underlying surface, an underlying surface elevation, etc.

The effective method (referred to as an image functionalization method) of an optical flow evaluation is stated in the report. The functionalization method differs from the well know gradient method in operating not upon the image intensity functions but upon values of a special functional, determined on a set of the image intensity functions. On the base of that approach a functional relation equation is derived. That equation is an analogue of a brightness constancy constraint equation used in the gradient method of image registration, but it does not hold spatial derivatives of image density functions. That brings considerably new features of universality and accuracy to the technique of the image motion parameters estimation as the equation encloses spatial derivatives of the applied functional kernel only. The functional relation equation establishes a fundamental linkage between measurable characteristics of dynamic images and its motion parameters. It represents a generalization of gradient group methods. This method is free from main principal shortcomings of the ordinary gradient method. As a result the method gives an opportunity to solve different difficult problems of registration such as varying brightness images registration, different color images interconnecting and others.)

We study the topological structure of $SU(3)$ lattice gluodynamics by cluster analysis. This methodological study is meant as preparation for full QCD. The topological charge density is becoming visible in the process of overimproved gradient flow, which is monitored by means of the the Inverse Participation Ratio (IPR). The flow is stopped at the moment when calorons dissociate into dyons due to the overimproved character of the underlying action. This gives the possibility to simultaneously detect all three dyonic constituents of KvBLL calorons in the gluonic field. The behaviour of the average Polyakov loop under (overimproved) gradient flow could be also (as its value) a diagnostics for the actual phase the configuration is belonging to. Timelike Abelian monopole currents and specific patterns of the local Polyakov loop are correlated with the topological clusters.The spectrum of reconstructed cluster charges $Q_{cl}$ corresponds to the phases. It is scattered around $Q_{cl} \approx \pm 1/3$ in the confined phase, whereas it is $Q_{cl} \approx \pm 0.5 ��0.7$ for heavy dyons and $|Q_{cl}| < 0.3$ for light dyons in the deconfined phase. Heavy dyons are increasingly suppressed with increasing temperature. The paper is dedicated to the memory of Michael Mueller-Preussker who was a member of our research group for more than twenty years., 7 pages, 6 figures

Dileptons represent a unique probe for nuclear matter under extreme conditions reached in heavy ion collisions. They allow the study of meson properties, like mass and decay width, at various density and temperature regimes. Up to now, in the Tubingen model for dilepton production, modification of meson properties in nuclear medium has been accounted for by allowing a density dependence of the mass (Brown-Rho scaling) together with an ad hoc dependence of the meson decay widths on the same variable. We use the extended vector meson dominance (eVMD) model to extract meson properties in nuclear matter by computing the in-medium meson spectral functions. Dilepton spectra for C+C at 1.0 and 2.0 AGeV are calculated and compared with previous results.

We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We confirm the loss of confinement in both cases and investigate in what respect the modified ensembles differ from the confining ones from the point of view of the complementary confinement scenario.

This article in honor of Yurii Antonovich Simonov’s 70th birthday reviews some recent work related to the semiclassical approach to QCD at finite temperature based on classical solutions with nontrivial holonomy. By cooling Monte Carlo generated lattice SU(2) gauge fields, we investigate approximate solutions of the classical field equations as a possible starting point for rethinking the semiclassical approximation of the path integral. We show that old findings of cooling have to be reinterpreted in terms of Kraan-van Baal solutions with generically nontrivial holonomy instead of Harrington-Shepard caloron solutions with trivial holonomy. The latter represent only a subclass of possible topological configurations and for T < Tc seem to become suppressed due to quantum fluctuations.

We discuss recent solutions for SU(2) calorons with non-trivial holonomy at higher charge, both through analytic means and using cooling, as well as extensive lattice studies for SU(3)., 12 pages, 16 figures in 34 parts, 4 talks presented at Lattice 2004(topology)

Weak radiative decay Λ → ne+e− depends in general on four independent electromagnetic transition form factors. These form factors can be fixed in an extended model of dominance of vector mesons, where the asymptotic behavior of form factors is in agreement with quark counting rules. The dependence of the branching ratio of the Λ → ne+e− decay on the relative weight of four electromagnetic form factors is investigated.

The Dalitz plot distribution of the $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ decay is determined by using a data sample of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{7}$ $\ensuremath{\eta}$ mesons from the $pd\ensuremath{\rightarrow}^{3}\mathrm{He}\ensuremath{\eta}$ reaction at 1 GeV collected by the WASA detector at COSY.

The production of d' dibaryons in heavy ion collisions due to the elementary process NN -> d' + pion is considered. The cross section NN -> d' + pion is estimated using the vacuum d' width = 0.5 MeV extracted from data on the double charge exchange reactions on nuclei. The d' production rate per single collision of heavy ions is estimated at an incident beam energy of 1 A GeV within the framework of the Quantum Molecular Dynamics transport model. We suggest to analyse the invariant mass spectrum of the NN + pion system in order to search for an abundance of events with the invariant mass of the d' dibaryon. The d' peak is found to exceed the statistical fluctuations of the background at a level of 6 standard deviations for 2 10^5 A central collisions of heavy ions with the atomic number A., 29 pages including 7 figures, REVTeX

The hypothesis of leptonic charge raises the problem of its neutralization, which is crucial for the stability of material bodies. The screening of the leptonic charge by a charged bosonic condensate is considered. The screening length and the structure of the skin layer are investigated in both the nonrelativistic and relativistic regimes.

The effects of the presence of $\Delta$-isobars in nuclear matter are studied in the framework of relativistic mean-field theory. The existence of stable nuclei at saturation density imposes constraints on the $\Delta$-isobar self-energy and thereby on the mean-field coupling constants of the scalar and vector mesons with $\Delta$-isobars. The range of possible values for the scalar and vector coupling constants of $\Delta$-isobars with respect to the nucleon coupling is investigated and compared to recent predictions of QCD sum-rule calculations., Comment: 8 pages, Latex using Elsevier style, 2 PS figures, minor changes in revised version

An experimental Dalitz plot distribution for the decay η → π+π−π0 is fitted by the theoretical one obtained in chiral perturbation theory with unitarity corrections taken into account. The fit shows that the difference of light-quark masses is larger than is expected from electromagnetic mass differences of neutral and charged kaons.

Using a standard cooling method for SU(3) lattice gauge fields constant Abelian magnetic field configurations are extracted after dyon-antidyon constituents forming metastable Q=0 configurations have annihilated. These so-called Dirac sheets, standard and non-standard ones, corresponding to the two U(1) subgroups of the SU(3) group, have been found to be stable if emerging from the confined phase, close to the deconfinement phase transition, with sufficiently nontrivial Polyakov loop values. On a finite lattice we find a nice agreement of the numerical observations with the analytic predictions concerning the stability of Dirac sheets depending on the value of the Polyakov loop.

The extended vector meson dominance model, which allows one to describe the electromagnetic form factors of nucleons obeying the asymptotic quark counting rule prescriptions and contains the minimal number of free parameters, is presented. We obtain a reasonable fit of form factors over the experimentally available spacelike region of momentum transfer and reasonable results in the timelike region.

We reveal the center vortex content of SU(2) calorons and ensembles of them. We use Laplacian center gauge as well as maximal center gauges to show that the vortex in a single caloron consists of two parts. The first one connects the constituent dyons of the caloron (which are monopoles in Laplacian Abelian gauge) and extends in time. The second part is predominantly spatial, encloses one of the dyons and can be related to the twist in the caloron gauge field. This part depends strongly on the caloron holonomy and degenerates to a plane when the holonomy is maximally nontrivial, i.e. when the asymptotic Polyakov loop is traceless. Correspondingly, we find the spatial vortices in caloron ensembles to percolate in this case. This finding fits perfectly in the confinement scenario of vortices and shows that calorons are suitable to facilitate the vortex confinement mechanism.

We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We find that the zero modes and the band of nonzero modes close to zero disappear from the spectrum of the overlap Dirac operator, confirming the absence of topological charge and quark condensate. The different behavior of the modified ensembles under smearing compared to the unmodified Monte Carlo ensemble corroborates these findings. The gluonic topological susceptibility rapidly approaches zero in accordance with ${Q}_{\mathrm{index}}=0$. The remaining (ultraviolet) monopoles without vortices and\char22{}to a less extent\char22{}the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble affects the monopoles and vortices only by smoothing, reducing the density only slightly.

We report on a self-consistent calculation of the in-medium spectral functions of the rho and omega mesons at finite baryon density. The corresponding in-medium dilepton spectrum is generated and compared with HADES data. We find that an iterative calculation of the vector meson spectral functions provides a reasonable description of the experimental data., Comment: Talk given at International School of Nuclear Physics, 30th Course, "Heavy Ion Collisions from the Coulomb Barrier to the Quark Gluon Plasma", Erice, Italy, 16-24 Sep 2008

We describe classical spinning particles in external fields. This formalism is extended to spinning particles localized at the ends of open Nambu strings. We consider the relations between the frequencies of spin precession and the energy of spin-orbit splitting.

The phase-space paths introduced by Cheuk-Yin Wong in Phys. Rev.C25, 1460 (1982) and discussed recently in the literature can be used for calculation of evolution of the Wigner function to first order in the time increments only. The first-order solutions are helpful to determine the phase-space Green function in the framework of the phase-space path integral method., 2 pages, accepted to publication in PRC, section Comments

In this talk, relying on experience with various lattice filter techniques, we argue that the semiclassical structure of finite temperature gauge fields for T < T_c is dominated by calorons with non-trivial holonomy. By simulating a dilute gas of calorons with identical holonomy, superposed in the algebraic gauge, we are able to reproduce the confining properties below T_c up to distances r = O(4 fm} >> ��(the caloron size). We compute Polyakov loop correlators as well as space-like Wilson loops for the fundamental and adjoint representation. The model parameters, including the holonomy, can be inferred from lattice results as functions of the temperature., Talk by M. M\"uller-Preussker at "Quark Confinement and Hadron Structure VII", Ponta Delgada, Azores, Portugal, September 2 - 7, 2006, 4 pages, 2 figures, to appear in the Proceedings

Institute for Theoretical and Experimental Physics,B. Cheremushkinskaya 25, Moscow 117259, RussiaIn equilibrium, at finite temperature below and above the deconfining phase transition, we havegenerated lattice SU(2) gauge fields and have exposed them to smearing in order to investigate theemerging clusters of topological charge. Analysing in addition the monopole clusters according tothe maximally Abelian gauge, we have been able to characterize part of the topological clusters tocorrespond either to non-static calorons or static dyons in the context of Kraan-van Baal caloronsolutions with non-trivial holonomy. We show that the relative abundance of these calorons anddyons is changing with temperature and offer an interpretation as dissociation of calorons into dyonswith increasing temperature. The profile of the Polyakov loop inside the topological clusters and the(model-dependent) accumulated topological cluster charges support this interpretation. Above thedeconfining phase transition light dyons (according to Kraan-van Baal caloron solutions with almosttrivial holonomy) become the most abundant topological objects. They are presumably responsiblefor the magnetic confinement in the deconfined phase.

We calculate the in-medium $D$ meson self-energies in a hot pion gas induced by resonance interactions with pions. The appropriate resonances in the {\it s},~ {\it p} and {\it d} waves of the $D$ meson-pion pair are represented by low lying scalar, vector and tensor $D^*$ mesons. At temperatures around 200 MeV the D-meson mass drops by $30~ \rm {MeV}$ and the scattering width grows up to $60~ \rm {MeV}$. Similar medium effects are found for the $D^*$ vector mesons. This opens and/or enhances the decay and/or dissociation channels of the charmonium states $\Psi^\prime$, $\chi_c$ and $J/\Psi$ to $D \bar D,~D^* \bar D,~D \bar D^* ,~D^* \bar D^*$ pairs in pion matter., Comment: 5 pages Revtex, 4 eps figures, final version accepted for publication in PRC

We report on our search for Kraan-van Baal calorons in finite temperature SU(2) lattice ensembles. We also discuss recent progress made in developing a caloron-anticaloron gas model decribing confinement and deconfinement in the context of trivial and non-trivial holonomy.

Using smearing of equilibrium lattice fields generated at finite temperature in the confined phase of $SU(2)$ lattice gauge theory, we have investigated the emerging topological objects (clusters of topological charge). Analyzing their monopole content according to the Polyakov gauge and the maximally Abelian gauge, we characterize part of them to correspond to nonstatic calorons or static dyons in the context of Kraan-van Baal caloron solutions with nontrivial holonomy. The behavior of the Polyakov loop inside these clusters and the (model-dependent) topological charges of these objects support this interpretation.

We consider the {theta}{sup +}(1540) pentaquark in the string model that correctly reproduces the linear Regge trajectories for the case of orbtal excitations of light qq mesons and qqq baryons. Assuming (and arguing in favor of) the diquark-antiquark-diquark ([ud]s[ud]) clustering of this orbitally excited object we found its mass about 290 MeV above the experimental value 1540 MeV. In the model considered this discrepancy could be attributed to the change of the constituent mass of s antiquark as compared to that of s quark localized at the string end.

The mean field (MF) approximation for the pion matter, being equivalent to the leading ChPT order, involves no dynamical loops and, if self-consistent, produces finite renormalizations only. The weight factor of the Haar measure of the pion fields, entering the path integral, generates an effective Lagrangian $\delta \mathcal{L}_{H}$ which is generally singular in the continuum limit. There exists one parameterization of the pion fields only, for which the weight factor is equal to unity and $\delta \mathcal{L}_{H}=0$, respectively. This unique parameterization ensures selfconsistency of the MF approximation. We use it to calculate thermal Green functions of the pion gas in the MF approximation as a power series over the temperature. The Borel transforms of thermal averages of a function $\mathcal{J}(\chi ^{\alpha}\chi ^{\alpha})$ of the pion fields $\chi ^{\alpha}$ with respect to the scalar pion density are found to be $\frac{2}{\sqrt{\pi}}\mathcal{J}(4t)$. The perturbation series over the scalar pion density for basic characteristics of the pion matter such as the pion propagator, the pion optical potential, the scalar quark condensate $$, the in-medium pion decay constant ${\tilde{F}}$, and the equation of state of pion matter appear to be asymptotic ones. These series are summed up using the contour-improved Borel resummation method. The quark scalar condensate decreases smoothly until $T_{max}\simeq 310$ MeV. The temperature $T_{max}$ is the maximum temperature admissible for thermalized non-linear sigma model at zero pion chemical potentials. The estimate of $T_{max}$ is above the chemical freeze-out temperature $T\simeq 170$ MeV at RHIC and above the phase transition to two-flavor quark matter $T_{c} \simeq 175$ MeV, predicted by lattice gauge theories., Comment: Replaced with revised and extended version. Results are compared to lattice gauge theories. 16 pages REVTeX, 13 eps figures

We use $\ensuremath{\epsilon}$-cooling, adjusting at will the order ${a}^{2}$ corrections to the lattice action, to study the parameter space of instantons in the background of nontrivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero-temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by ``adiabatically'' adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyze these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.

Using cooling for SU(2) lattice configurations, purely Abelian constant magnetic-field configurations were left over after the annihilation of constituents that formed metastable $Q=0$ configurations. These so-called Dirac sheet configurations were found to be stable if emerging from the confined phase, close to the deconfinement phase transition, provided their Polyakov loop was sufficiently nontrivial. Here we show how this is related to the notion of marginal stability of the appropriate constant magnetic-field configurations. We find a perfect agreement between the analytic prediction for the dependence of stability on the value of the Polyakov loop (the holonomy) in a finite volume and the numerical results studied on a finite lattice in the context of the Dirac sheet configurations.

We consider the exclusive reaction $pp\ensuremath{\rightarrow}pp{\ensuremath{\pi}}^{0}{e}^{+}{e}^{\ensuremath{-}}$ at energies near the $\ensuremath{\eta}$ production threshold. Different channels contribute to this reaction. One of them\char22{}the production of $\ensuremath{\eta}$ mesons and its subsequent rare decay $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{e}^{+}{e}^{\ensuremath{-}}$\char22{}is considered as a signal to which the other channels constitute the background. The conditions under which the signal can be larger than background are investigated.

The exclusive $\phi$ meson production in proton-proton reactions is calculated within the resonance model. The considered model was already successfully applied to the description of $\pi$, $\eta$, $\rho$, $\omega$, $\pi\pi$ production in proton-proton collisions. The only new parameter entering into the model is the $\omega-\phi$ mixing angle $\theta_{mix}$ which is taken equal to $\theta_{mix} \approx 3.7^o$., Comment: 7 pages, 1 figure, to appear in the brief report section of PRC

We report the observation of calorons with nontrivial holonomy and fractional topological charge objects in cooled lattice samples derived from SU(2) equilibrium ensembles at $T, Comment: 3 pages, 3 figures, talk given at Confinement V, Gargnano, Italy, 10-14 Sep 2002. References and acknowlegements added

We discuss Kraan - van Baal - Lee - Lu (KvBLL) solutions of the classical Yang-Mills equations with temperature in the context of SU(3) lattice gauge theory. We present discretized lattice versions of KvBLL solutions and other dyonic structures, obtained by cooling in order to understand their variety and signature. An analysis of the zero modes of the lattice Dirac operator for different fermionic boundary conditions gives clear evidence for a KvBLL-like background of finite T lattice subensembles with Q = +/-1. Using APE-smearing we are able to study the topological charge density q(x) of the configurations and to corroborate this interpretation., Comment: Presented at LATTICE 2003 (topology) by C. Gattringer and E.M. Ilgenfritz, 6 pages

Finite temperature Euclidean SU(2) lattice gauge fields generated in the confinement phase close to the deconfinement phase transition are subjected to cooling. The aim is to identify long-living, almost-classical local excitations which carry (generically non-integer) topological charge. Two kinds of spatial boundary conditions (fixed holonomy and standard periodic boundary conditions) are applied. For the lowest-action almost-classical configurations we find that their relative probability semi-quantitatively agrees for both types of boundary conditions. We find calorons with unit topological charge as well as (anti-)selfdual lumps (BPS-monopoles or dyons) combined in pairs of non-integer (equal or opposite sign) topological charge. For calorons and separated pairs of equal-sign dyons obtained by cooling we have found that (i) the gluon field is well-described by Kraan-van Baal solutions of the Euclidean Yang-Mills field equations and (ii) the lowest Wilson-fermion modes are well-described by analytic solutions of the corresponding Dirac equation. For metastable configurations found at higher action, the multi-center structure can be interpreted in terms of dyons and antidyons, using the gluonic and fermionic indicators as in the dyon-pair case. Additionally, the Abelian monopole structure and field strength correlators between the centers are useful to analyse the configurations in terms of dyonic constituents. We argue that a semi-classical approximation of the non-zero temperature path integral should be built on superpositions of solutions with non-trivial holonomy.

With the help of the cooling method applied to SU(2) lattice gauge theory at non-zero $T \le T_c$ we present numerical evidence for the existence of superpositions of Kraan-van Baal caloron (or BPS monopole pair) solutions with non-trivial holonomy, which might constitute an important contribution to the semi-classical approximation of the partition function., Comment: 3 pages, 6 figures, contribution to Lattice2002(topology)

We generate SU(2) lattice gauge fields at finite temperature and cool them in order to characterize the two phases by the occurrence of specific classical solutions.We apply two kinds of spatial boundary conditions: fixed holonomy and standard periodic b.c. For T < T_c our findings concerning classical configurations semi-quantitatively agree for both types of boundary conditions. We find in the confinement phase a mixture of undissociated calorons with lumps of positive or negative half-integer topological charges., Lattice2001(confinement)

Relativistic, kinematically complete phenomenological expressions for the dilepton decay rates of nucleon resonances with arbitrary spin and parity are derived in terms of the magnetic, electric, and Coulomb transition form factors. The dilepton decay rates of the nucleon resonances with masses below 2 GeV are estimated using the extended vector meson dominance model for the transition form factors. The model provides a unified description of the photo- and electroproduction data, the vector meson decays, and the dilepton decays of the nucleon resonances. The constraints on the transition form factors from the quark counting rules are taken into account. The parameters of the model are fixed by fitting the available photo- and electroproduction data and using results of the multichannel partial-wave analysis of the $\pi N$ scattering. Where experimental data are not available, predictions of the non-relativistic quark models are used as an input. The vector meson coupling constants of the magnetic, electric, and Coulomb types are determined. The dilepton widths and the dilepton spectra from decays of nucleon resonances with masses below 2 GeV are calculated., Comment: An error in the code is found and fixed. Numerical results for the spin-half nucleon resonances changed. A few misprints are removed from the text. 56 pages including 7 tables and 27 eps figures, REVTeX

The field strength correlators at zero temperature are semi-classically evaluated fitting the random instanton liquid model to lattice data for quenched SU(3) lattice gauge theory. We restrict ourselves to the lowest order in an instanton density expansion necessary to explain the difference between transverse and longitudinal correlation functions. In the instanton-instanton and instanton-antiinstanton contributions the Schwinger line factors neglected in a previous analysis are numerically taken into account in a weighted Monte Carlo evaluation. This leads to different estimates for instanton size and density. A reasonable description of the correlators within the intermediate range from 0.4 fm to 1 fm is obtained., 20 pages, 3 figures

We study SU(2) lattice gauge theory at $T>0$ in a finite box with fixed holonomy value at the spatial boundary. We search for (approximate) classical solutions of the lattice field equations and find in particular the dissociated calorons recently discussed by van Baal and collaborators., Talk at Lattice 2000, Bangalore; 4 pages, 4 figures, LaTeX

Low temperature of the phase transition into the quark-gluon plasma correspond to low values of the bag model constant and to absolutely stable strange quark matter. Some of the observed pulsars are identified quite reliably as neutron stars. If strange matter is stable, the central density of these pulsars is to be smaller that critical density of the phase transition into the nonstrange quark matter. The nonstrange quark matter being formed turns to more stable strange matter on a weak interaction timescale converting neutron stars into strange stars. The requirement of stability of old and newly born neutron stars is used to constrain the bag model constant and the critical temperature of the phase transition into the quark-gluon plasma at zero chemical potential.

The possibility for occurrence of a Bose condensate of dibaryons in nuclear matter is investigated within the framework of the Walecka model in the mean-field approximation. Constraints for the omega - and sigma - meson coupling constants with dibaryons following from the requirement of stability of dibaryon matter against compression are derived and the effect of sigma - and pi - meson exchange current contributions to the sigma - dibaryon coupling constant is discussed. The mean-field solutions of the model are constructed. The effective nucleon mass vanishes when the density of dibaryons approaches a critical value about 0.15/fm^3. The Green's functions of the equilibrium binary mixture of nucleons and dibaryons are constructed by solving the Gorkov-Dyson system of equations in the no-loop approximation. We find that when the square of the sound velocity is positive, the dispersion laws for all elementary excitations of the system are real functions. This indicates stability of the ground state of the heterophase nucleon-dibaryon mixture. In the model considered, production of dibaryons becomes energetically favorable at higher densities as compared to estimates based on a model of non-interacting nucleons and dibaryons., Comment: 35 pages, 15 figures

The hypothetical leptonic photons, namely, those that have coupling to electrons, can be produced in the Sun and other stellar objects by the process of photoproduction. Being weakly interacting particles they could substantially influence the evolution of the star by changing the process of heat release. In order for this not to happen, the leptonic coupling constant must be smaller than ∼10−26, i.e., much smaller than the ∼10−12 required for the stability of bodies against the leptonic Coulomb forces.

The problem of the skin layer for the screening of the leptonic charge of a body by condensed bosons is considered.