Abstract:
The interaction of dyons in the mean field approximation is considered. The result of interaction is the mass term for dyonic field in the effective Lagrangian. Due to the mass term the profile function of dyon falls off exponentially at large distances.

Abstract:
The following lectures concern with the quark structure of hadrons made up from light quarks. The symmetries of strong interaction were the only instruments used for the description of this structure. The models of hadrons (there are a lot of them) were not considered. There was not also considered the structure of hadrons with heavy quarks. The first round of problems (models of hadrons) is not considered because of its unexhaustability. The second round of problems (hadrons with heavy quarks) is not considered because of the physics of heavy flavors tends mainly to electroweak interaction and will be considered in the course of electroweak interactions. Therefore, the presented here course, being the self-bounded part of the theory of elementary particles, is considered separately. These lectures were formed from 1989 and are the part of the set of courses on the theory of fundamental interactions for the students of Moscow Physical Technical Institute. The basic source of the lectures was the unpublished manuscript "Hadrons and quarks" by L.B. Okun. Another source was the "Lectures on the theory of unitary symmetry in elementary particle physics" by Nguen Van Hieu (Atomizdat, Moscow 1967). The list of references (due to its smallness) is absent.

Abstract:
If strange matter is absolutely stable, the ordinary nuclei decay to strangelets, while neutron stars convert into strange stars. Lifetimes of the ordinary nuclei are constrained experimentally to be above $\sim 10^{33}$ years, while lifetimes of the metastable neutron stars depend on the neutron star masses and can exceed the age of the Universe. As a consequence, the neutron stars and the strange stars can coexist in the Universe. We point out that numerical simulations of the conversion of neutron stars to strange stars, performed by M. Herzog and F. K. Roepke in Phys. Rev. D 84, 083002 (2011) [arXiv:1109.0539], are focused on a region in the parameter space of strange matter, in which low-mass neutron stars and strange stars are coexistent, whereas massive neutron stars are unstable and short lived on an astronomical timescale.

Abstract:
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.

Abstract:
The pion optical potential generated by the hypothetical pi-NN-coupled NN-decoupled dibaryon resonance d'(2065) is calculated to the lowest order in nuclear matter density. The contribution to the pion optical potential is found to be within the empirical errors, so the d'(2065) existence currently does not contradict to the observed properties of the pi-nucleus bound states. Future progress in the pionic X-ray spectroscopy can reveal contributions of pi-NN resonances to energy levels and widths of the pionic atoms.

Abstract:
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.

Abstract:
Kaon in-medium masses and mean-field potentials are calculated in isotopically symmetric pion matter to one loop of chiral perturbation theory. The results are extended to RHIC temperatures using experimental data on $\pi K$ scattering phase shifts. The kaon in-medium broadening results in an acceleration of the $\phi \to K\bar{K}$ decay. The increased apparent dilepton branching of the $\phi $-mesons, observed recently by NA50, NA49, and the PHENIX collaborations at RHIC, is interpreted in terms of rescattering of secondary kaons inside of the pion matter.

Abstract:
The inclusive reactions $pp \rightarrow e^+ e^- X$ and $np \rightarrow e^+ e^- X$ at the laboratory kinetic energy of 1.25 GeV are investigated in a model of dominance of nucleon and $\Delta$ resonances. Experimental data for these reactions have recently been reported by the HADES Collaboration. In the original model, the dileptons are produced either from the decays of nucleon and $\Delta$ resonances $R \rightarrow N e^+ e^-$ or from the Dalitz decays of $\pi^0$- and $\eta$-mesons created in the $R \to N\pi^0$ and $R \to N\eta$ decays. We found that the distribution of dilepton invariant masses in the $pp \rightarrow e^+ e^- X$ reaction is well reproduced by the contributions of $R \rightarrow N e^+ e^-$ decays and $R \rightarrow N \pi^0$, $\pi^0 \to \gamma e^+e^-$ decays. Among the resonances, the predominant contribution comes from the $\Delta(1232)$, which determines both the direct decay channel $R \rightarrow N e^+ e^-$ and the pion decay channel. In the collisions $np \rightarrow e^+ e^- X$, additional significant contributions arise from the $\eta$-meson Dalitz decays, produced in the $np \rightarrow np\eta$ and $np \rightarrow d\eta$ reactions, the radiative capture $np \rightarrow d e^+ e^-$, and the $np \rightarrow np e^+ e^-$ bremsstrahlung. These mechanisms may partly explain the strong excess of dileptons in the cross section for collisions of $np$ versus $pp$, which ranges from 7 to 100 times for the dilepton invariant masses of 0.2 to 0.5 GeV.

Abstract:
Topological objects of $SU(3)$ gluodynamics are studied at the infrared scale near the transition temperature with the help of zero and near-zero modes of the overlap Dirac operator. We construct UV filtered topological charge densities corresponding to three versions of the temporal boundary condition applied to this operator, for which the zero mode is known to be located on corresponding three constituent dyons (antidyons) in the reference case of an analytical (anti)caloron solution. The clustering of the three topological charge densities marks the positions of three types of dyons and antidyons which can therefore be considered as present in equilibrium (Monte Carlo) gluonic fields at the given resolution scale. We classify them either as constituents of nondissociated (anti)calorons or as constituents of (anti)dyon pairs or as isolated (anti)dyons. The pattern of the Polyakov loop describing the centers and the interior of these clusters is observed after a limited number of overimproved cooling steps and resembles the description known from analytical caloron solutions.

Abstract:
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 $<{\bar{q}}q>$, 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.