The spherically symmetric solution in Einstein-Dirac gravity is considered where the space section is the Hopf bundle. We use two Weyl spinors to obtain diagonal energy-momentum tensor that is necessary to have spherically symmetric gravitating solution. The solution for non-gravitating Dirac equation on the background of Lorentzian spacetime with the Hopf bundle as the space section are obtained also. Non-gravitating solutions for Dirac equation are defined by two half integer numbers $m$, $n$. The spherically symmetric gravitating solution for Einstein-Dirac equations are defined by $m = 0$, $n = 1/2$.
The subject of this work is the development of PIMC algorithms in various fields of quantum theory and condensed matter physics and their application for some important problems of physics. A high-performance muti-level algorithm is designed for many-body quantum systems calculations. This algorithm is applied for a computation of a metal hydrogen model. Within this model equations of state are obtained in a wide range of densities and temperatures. A first kind phase transition between liquid and bcc cubic crystal is detected and explored. A correct algorithm of PIMC calculations for relativistic quantum theory is also designed.
Presentation
It was proved that using quadratically integrable real radial wave functions of relativistic equation of SH type with effective potential of Schwarzschild field there exist degenerate stationary state of spin $1/2$ particles with the energy $E=0$. The bound energy $E_b=mc^2$ does not depend on quantum numbers $j$, $l$ and is the same for any gravity constant value. The particles with $E=0$ are very probably on some distance from the event horizon starting from zero up to few Compton wave lengths of the fermion depending on the gravity constant value. This work announces analogous solutions for degenerate bound states of fermions in Reissner-Nordström, Kerr, Kerr-Newman fields. The atom-like systems – collapsars with specific number of fermions in degenerate state are – are proposed as dark matter particles.
The process $e^{+}e^{-}\rightarrow\gamma^{*}\rightarrow \pi^{0}\gamma$ was considered using time-like pion transition form factor, obtained in the approach of the Anomaly Sum Rules(ASR). The total cross section and angular distribution of the process was calculated. As the result of the comparison with the data it was shown that ASR approach provides their good description in the regions far from the pole. Also there was proposed a method allowing to give reasonable description of data in the region of pole within the ASR approach. The strong restrictions for the parameters of the modified ASR approach were obtained.
We present the implementation of four-boson processes ($\gamma\gamma\to\gamma\gamma$, $Z\gamma\gamma\gamma\to 0$, $\gamma\gamma\to ZZ$) and the process $ud\to WA$ into SANC system. The calculations performed within Standard Model at one-loop level of accuracy keeping all the masses. We describe the diagrams of the processes, pre-calculation blocks, covariant and spiral amplitudes, special J-functions and $D_0$, $C_0$ functions of Passarino--Veltman, results of numerical calculations and their comparison, obtained with the use of SANC modules.
Presentation
We performed a detailed analysis of radiative decay of sterile neutrino with mass of few dozens of keV in strong magnetic field and degenerate electronic plasma. The calculation was performed with taking into account photon dispersion relation in external active environment. The influence of electron concentration to radiative decay probability was investigated. In was shown that the presence of strong electromagnetic field weakens strong catalytic influence of plasma to decay probability.
We performed the analysis of influence of magnetic field to the properties of massive neutrino. The general expression of self-energy operator of neutrino in external magnetic field of arbitrary intensity was obtained. This expression holds under arbitrary relation between neutrino masses and charged lepton and W-boson masses. Using this mass operator we found the expression for additional energy which neutrino gains in external magnetic field. On the basis of this expression for additional energy we obtained quantum field correction to magnetic moment of neutrino.
The vertex function of virtual massive neutrino in the limit of soft real photons was calculated. During this calculation we used the method which is based on the usage of self energy neutrino operator which was calculated in linear approximation over external electromagnetic field. We showed that electric charge and electric dipole moment of real massive neutrino turns to zero and non-zero value possesses its magnetic moment.
Presentation
The procedure of nonperturbative (NP) quantization a la Heisenberg is considered. NP quantization is based on a operator field equation for corresponding field theory. For example, for quantum chromodynamics (QCD) it will be Yang - Mills equation where all quantities becomes operators. We have not any prescriptions to solve such equation. In order to do that we use a set of equations for all possible Green’s functions. All Green’s functions give us full information about the quantum state and field operators properties. Practically such equations set can not be solved analytically and we have to use some approximation method. The approximate approach for a NP quantization being suggested here is to derive approximations for unknown Green’s functions using the properties of the quantum system under consideration so that a sufficient number of equations exists. In making such approximations, we close an infinite set of equations for the Green’s functions. The comparison with turbulence modeling is performed.
We give an overview of our recent results in studying two most important and widely discussed quantum processes: electron-positron pairs production off a probe photon propagating through a polarized short-pulsed electromagnetic (e.g. laser) wave field or generalized Breit-Wheeler process, and single a photon emission off an electron interacting with the laser pules, so-called non-linear Compton scattering. We show that the probabilities of particle production in both processes are determined by interplay of two dynamical effects, where the first one is related to the shape and duration of the pulse and the second one is non-linear dynamics of the interaction of charged fermions with a strong electromagnetic field. Special attention is done to determination of the pulse carrier phase. We elaborate suitable expressions for the production probabilities and cross sections, convenient for studying evolution of the plasma in presence of strong electromagnetic fields.
Presentation
The full and differential width of the decay $\tau \to K^0 K^- \nu_\tau$ are calculated in the framework of the extended Nambu–Jona-Lasinio model. The contributions of the subprocesses with the intermediate vector mesons $\rho(770)$ and $\rho(1450)$ are taken into account. The obtained results are in satisfactory agreement with the experimental data.
In order to prove the existence of a critical end point (CEP) in the QCD phase diagram it is sufficient to demonstrate that at zero temperature $T=0$ a first order phase transition exists as a function of the baryochemical potential $\mu$, since it is established knowledge from ab-initio lattice QCD simulations that at $\mu=0$ the transition on the temperature axis is a crossover.
We present the argument that the observation of a gap in the mass-radius relationship for compact stars which proves the existence of a so-called third family (aka "mass twins") will imply that the $T=0$ equation of state of compact star matter exhibits a strong first order transition with a latent heat that satisfies $\Delta\epsilon/\epsilon_c > 0.6$. Since such a strong first order transition under compact star conditions will remain first order when going to symmetric matter, the observation of a disconnected branch (third family) of compact stars in the mass-radius diagram proves the existence of a CEP in QCD. Modeling of such compact star twins is based on a QCD motivated NJL quark model with high order interactions together with the hadronic DD2-MEV model fulfilling nuclear observables.
Furthermore we show results of a Bayesian analysis (BA) using disjunct M-R constraints for extracting probability measures for cold, dense matter equations of state. In particular this study reveals that measuring radii of the neutron star twins has the potential to support the existence of a first order phase transition for compact star matter.
In this talk one can find the review of applications of method of effective potentials of Dirac equation in external gravitational and electromagnetic fields. During the analysis of quantum mechanical movement of charged particle with spin 1/2 in the external Coulomb's field by the method of effective potentials of Dirac equation we found unpenetrable barrier which was not studied before. This barrier exists only when the signs of particle charge and of the Coulomb's field are the same. For particle at rest the barrier radius is equal to the half of its classical radius. When energy of particle grows the radius of this barrier decreases. In the talk we give some practical conclusions from the fact of this barrier existence. The results of this work can be used as a tests for developing models of lepton inner structure.
The decays $\tau \to (\eta,\eta') K^- \nu_\tau$ are described in the framework of the extended Nambu-Jona-Lasinio model. Both full and differential widths of these decays are calculated. The vector and scalar channels are considered. In the vector channels, the subprocesses with intermediate $K^*(892)$ and $K^{*’}(1410)$ mesons play the main role. In the scalar channels, the subprocesses with intermediate $K^{0*}(800)$ and $K^{0*’}(1430)$ mesons are considered. Scalar channels play a less important role in calculation of the full width of the $\tau$-decay. The results are in satisfactory agreement with the experimental data.
Our final goal is to show the relation between the chiral symmetry breaking and the quark confinement which is caused by the monopole condensation. In order to show the relation, we add one pair of monopoles with magnetic charges to QCD vacuum by a monopole creation operator, and investigate properties of the chiral symmetry breaking, using the Overlap fermion which preserves the chiral symmetry in the lattice gauge theory.
In previous work we have demonstrated that the additional monopoles form long loops, and create instantons in QCD vacuum [1]. In the study of the random matrix theory, we have found that the chiral condensate, which is the order parameter of the chiral symmetry breaking, decreases with increasing the magnetic charges of the additional monopoles [2]. That is to say that the monopoles are related with the chiral symmetry breaking.
However, these studies have mainly been done by adding monopoles to the small lattice volume and one lattice spacing. We have to check an influence of the finite lattice volume and discretization. Therefore, in the present work, we add monopoles with magnetic charges to the configurations of the larger lattice volumes and different parameters of lattice spacing, and study the relation between the chiral symmetry breaking, instantons, and monopoles [3].
In this seminar, I will introduce our research project, and present the results indicating that the monopoles are related with instantons and the chiral symmetry breaking.
[1] A. Di Giacomo and M. Hasegawa, Instantons and monopoles, Phys. Rev. D 91 (2015) 054512.
[2] A. Di Giacomo, M. Hasegawa, and F. Pucci, Chiral symmetry breaking and monopoles, arXiv:hep-lat/1510.07463 (2015), (PoS (CD15) 127).
[3] A. Di Giacomo and M. Hasegawa, Chiral symmetry breaking, instantons, and monopoles, arXiv:hep-lat/1512.00359 (2015), (PoS (LATTICE 2015) 313).