Particles — Open Access Journal

The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a local coordinate system allows us to detect new hidden symmetries of the internal motion of a dynamical system, which allows us to reduce the three-body problem to the 6th order system. A new approach makes the system of geodesic equations with respect to the evolution parameter of a dynamical system (internal time) fundamentally irreversible. To describe the motion of three-body system in different random environments, the corresponding stochastic differential equations (SDEs) are obtained. Using these SDEs, Fokker-Planck-type equations are obtained that describe the joint probability distributions of geodesic flows in phase and configuration spaces. The paper also formulates the quantum three-body problem in conformal-Euclidean space. In particular, the corresponding wave equations have been obtained for studying the three-body bound states, as well as for investigating multichannel quantum scattering in the framework of the concept of internal time. This allows us to solve the extremely important quantum-classical correspondence problem for dynamical Poincaré systems. Full article

In different areas of mechanics, highly non-equilibrium processes are accompanied by self-organization of various type turbulent structures and localized inhomogeneities at intermediate scale between macro and micro levels. In order to describe the self-organization of the new dynamic structures on the mesoscale, a new problem formulation based on the results of non-equilibrium statistical mechanics, control theory of adaptive systems, and theory of a special type nonlinear operator sets is proposed. Determination of the turbulent structure parameters through constraints imposed on the system in the form of nonlinear functionals is an inverse problem similar to problems on spectra in quantum mechanics. Like in quantum mechanics, the bounded system in response to impact forms a discrete spectrum of the turbulent structure sizes and lifetimes which goes into continuous spectrum close-to-equilibrium. The proposed description of the structure evolution on the intermediate scale level which is valid far from thermodynamic equilibrium bridges the gap between macroscopic theories and quantum mechanics and affirms the unity of the physical laws of nature. Full article

The propagator of a gauge boson, like the massless photon or the massive vector bosons $W^{\pm }$ and Z of the electroweak theory, can be derived in two different ways, namely via Green’s functions (semi-classical approach) or via the vacuum expectation value of the time-ordered product of the field operators (field theoretical approach). Comparing the semi-classical with the field theoretical approach, the central tensorial object can be defined as the gauge boson projector, directly related to the completeness relation for the complete set of polarisation four-vectors. In this paper we explain the relation for this projector to different cases of the $R_{\xi }$ gauge and explain why the unitary gauge is the default gauge for massive gauge bosons. Full article

We present a brief review of general results about non-rotating neutron stars in simple $R^2$ gravity and its extension with a scalar axion field. Modified Einstein equations are presented for metrics in isotropical coordinates. The mass–radius relation, mass profile and dependence of mass from central density on various equations of state are given in comparison to general relativity. Full article

The internal degrees of freedom of fermions are in the spin-charge-family theory described by the Clifford algebra objects, which are superposition of an odd number of ${\gamma }^a$ ’s. Arranged into irreducible representations of “eigenvectors” of the Cartan subalgebra of the Lorentz algebra $S^{ab}$ $(=\frac{i}{2}{\gamma }^a{\gamma }^b{|}_{a\ne b})$ these objects form $2^{\frac{d}{2}-1}$ families with $2^{\frac{d}{2}-1}$ family members each. Family members of each family offer the description of all the observed quarks and leptons and antiquarks and antileptons, appearing in families. Families are reachable by ${\tilde{S}}^{ab}$ $=\frac{1}{2}{\tilde{\gamma }}^a{\tilde{\gamma }}^b{|}_{a\ne b}$ . Creation operators, carrying the family member and family quantum numbers form the basis vectors. The action of the operators ${\gamma }^a$ ’s, $S^{ab}$ , ${\tilde{\gamma }}^a$ ’s and ${\tilde{S}}^{ab}$ , applying on the basis vectors, manifests as matrices. In this paper the basis vectors in $d=(3+1)$ Clifford space are discussed, chosen in a way that the matrix representations of ${\gamma }^a$ and of $S^{ab}$ coincide for each family quantum number, determined by ${\tilde{S}}^{ab}$ , with the Dirac matrices. The appearance of charges in Clifford space is discussed by embedding $d=(3+1)$ space into $d=(5+1)$ -dimensional space. The achievements and predictions of the spin-charge-family theory is also shortly presented. Full article

In this paper, we discuss the damping of density oscillations in dense nuclear matter in the temperature range relevant to neutron star mergers. This damping is due to bulk viscosity arising from the weak interaction “Urca” processes of neutron decay and electron capture. The nuclear matter is modelled in the relativistic density functional approach. The bulk viscosity reaches a resonant maximum close to the neutrino trapping temperature, then drops rapidly as temperature rises into the range where neutrinos are trapped in neutron stars. We investigate the bulk viscous dissipation timescales in a post-merger object and identify regimes where these timescales are as short as the characteristic timescale ∼10 ms, and, therefore, might affect the evolution of the post-merger object. Our analysis indicates that bulk viscous damping would be important at not too high temperatures of the order of a few MeV and densities up to a few times saturation density. Full article

The relativistic mean field (RMF) model of the nuclear matter equation of state was modified by including the effect of Pauli-blocking owing to quark exchange between the baryons. Different schemes of a chiral enhancement of the quark Pauli blocking was suggested according to the adopted density dependence of the dynamical quark mass. The resulting equations of state for the pressure are compared to the RMF model DD2 with excluded volume correction. On the basis of this comparison a density-dependent nucleon volume is extracted which parameterizes the quark Pauli blocking effect in the respective scheme of chiral enhancement. The dependence on the isospin asymmetry is investigated and the corresponding density dependent nuclear symmetry energy is obtained in fair accordance with phenomenological constraints. The deconfinement phase transition is obtained by a Maxwell construction with a quark matter phase described within a higher order NJL model. Solutions for rotating and nonrotating (hybrid) compact star sequences are obtained, which show the effect of high-mass twin compact star solutions for the rotating case. Full article

The report presents the results of using the nonperturbative kinetic approach to describe the excitation of plasma oscillations in a graphene monolayer. As examples the constant electric field as well as an electric field of short high-frequency pulses are considered. The dependence of the induced conduction and polarization currents characteristics on the pulse intensity, pulse duration, and polarization is investigated. The characteristics of secondary electromagnetic radiation resulting from the alternating currents is investigated. The nonlinear response to the external electric field characterizes graphene as an active medium. Qualitative agreement is obtained with the existing experimental result of measurements of currents in constant electric fields and radiation from graphene in the case of excitation by means of the infrared and optical pulses. Full article

In search for an effective model of quark confinement we study the vacuum of SU(2) quantum chromodynamic with lattice simulations using Wilson action. Assuming that center vortices are the relevant excitations causing confinement, we analyzed their physical size and their color structure. We present confirmations for a vanishing thickness of center vortices in the continuum limit and hints at their color structure. This is the first time that algorithms for the detection of thick center vortices based on non-trivial center regions has been used. Full article

We discuss how the non-equilibrium process of pion production within the Zubarev approach of the non-equilibrium statistical operator leads to a theoretical foundation for the appearance of a non-equilibrium pion chemical potential for the pion distribution function for which there is experimental evidence in experiments at the CERN LHC. Full article

We aim to construct a potential better suited for studying quarkonium spectroscopy. We put the Cornell potential into a more geometrical setting by smoothly interpolating between the observed small and large distance behaviour of the quarkonium potential. We construct two physical models, where the number of spatial dimensions depends on scale: one for quarkonium with Cornell potential, another for unified field theories with one compactified dimension. We construct point charge potential for different dimensions of space. The same problem is studied using operator fractal calculus. We describe the quarkonium potential in terms of the point charge potential and identify the strong coupling fine structure constant dynamics. We formulate renormdynamics of the structure constant in terms of Hamiltonian dynamics and solve the corresponding motion equations by numerical and graphical methods, we find corresponding asymptotics. Potentials of a nonlinear extension of quantum mechanics are constructed. Such potentials are ingredients of space compactification problems. Mass parameter effects are motivated and estimated. Full article

The article considers a new mechanism of charge accumulation in the early Universe in theories with compact extra dimensions. The relaxation processes in the extra space metric that take place during its formation lead to the establishment of symmetrical extra space configuration. As a result, the initial accumulation of the number associated with the symmetry occurs. We demonstrate this mechanism using a simple example of a two-dimensional apple-like extra space metric with $U\left(1\right)$ -symmetry. The conceptual idea of the mechanism can be used to develop a model for the production of the baryon or lepton number in the early Universe. Full article

We present recent results on dynamical chiral symmetry breaking in (2 + 1)-dimensional QED with N four-component fermions. The results of the $1/N$ expansion in the leading and next-to-leading orders were found exactly in an arbitrary nonlocal gauge. Full article

The observed anomalous excess of high-energy cosmic ray (CR) positrons is widely discussed as possible indirect evidence for dark matter (DM). However, any source of cosmic positrons is inevitably the source of gamma radiation. The least model dependent test of CR anomalies interpretation via DM particles decays (or annihilation) is connected with gamma-ray background due to gamma overproduction in such processes. In this work, we impose an observational constraint on gamma ray production from DM. Then, we study the possible suppression of gamma yield in the DM decays into identical final fermions. Such DM particles arise in the multi-component dark atom model. The influence of the interaction vertices on the gamma suppression was also considered. No essential gamma suppression effects are found. However, some minor ones are revealed. Full article

The future “Facility for Antiproton and Ion Research” (FAIR) is an accelerator-based international center for fundamental and applied research, which presently is under construction in Darmstadt, Germany. An important part of the program is devoted to questions related to astrophysics, including the origin of elements in the universe and the properties of strongly interacting matter under extreme conditions, which are relevant for our understanding of the structure of neutron stars and the dynamics of supernova explosions and neutron star mergers. The Compressed Baryonic Matter (CBM) experiment at FAIR is designed to measure promising observables in high-energy heavy-ion collisions, which are expected to be sensitive to the high-density equation-of-state (EOS) of nuclear matter and to new phases of Quantum Chromo Dynamics (QCD) matter at high densities. The CBM physics program, the relevant observables and the experimental setup will be discussed. Full article

We study the transverse and longitudinal gluon propagators in the Landau-gauge lattice QCD with gauge group $SU\left(2\right)$ at nonzero quark chemical potential and zero temperature. We show that both propagators demonstrate substantial dependence on the quark chemical potential. This observation does not agree with earlier findings by other groups. Full article

With the aim of understanding the phase structure of nuclear matter created in high-energy nuclear collisions at finite baryon density, a beam energy scan program has been carried out at Relativistic Heavy Ion Collider (RHIC). In this mini-review, most recent experimental results on collectivity, criticality and heavy flavor productions will be discussed. The goal here is to establish the connection between current available data and future heavy-ion collision experiments in a high baryon density region. Full article

The properties and mass distribution of the ultramagnetized atomic nuclei which arise in heavy-ion collisions and magnetar crusts, during Type II supernova explosions and neutron star mergers are analyzed. For the magnetic field strength range of 0.1–10 teratesla, the Zeeman effect leads to a linear nuclear magnetic response that can be described in terms of magnetic susceptibility. Binding energies increase for open shell and decrease for closed shell nuclei. A noticeable enhancement in theyield of corresponding explosive nucleosynthesis products with antimagic numbers is predicted for iron group and r-process nuclei. Magnetic enrichment in a sampleof ⁴⁴Ti corroborate theobservational results and imply a significant increase in the quantity of the main titanium isotope, ⁴⁸Ti, in the chemical composition of galaxies. The enhancement of small mass number nuclides in the r-process peak may be due to magnetic effects. Full article