An Efficient Method for the Solution of Schwinger–Dyson Equations for Propagators

Efficient computation methods are devised for the perturbative solution of Schwinger–Dyson equations for propagators. I show how a simple computation allows to obtain the dominant contribution in the sum of many parts of previous computations. This allows for an easy study of the asymptotic behavior of the perturbative series. In the cases of the four-dimensional supersymmetric Wess–Zumino model and the f₆³{\phi_6^3} complex scalar field, the singularities of the Borel transform for both positive and negative values of the parameter are obtained and compared.     

Delta Properties in the Rainbow-Ladder Truncation of Dyson–Schwinger Equations

We present a calculation of the three-quark core contribution to nucleon and Δ-baryon masses and Δ electromagnetic form factors in a Poincaré-covariant Faddeev approach. A consistent setup for the dressed-quark propagator, the quark–quark, quark–’diquark’ and quark–photon interactions is employed, where all ingredients are solutions of their respective Dyson–Schwinger or Bethe–Salpeter equations in a rainbow-ladder truncation. The resulting Δ electromagnetic form factors concur with present experimental and lattice data.     

A Method of Controlling Synchronization in Different Systems

A new control method to synchronize between two different systems is proposed and the mathematical proof of this method is provided. Moreover, numerical simulation validates the efficiency of the proposed method.     

Masses of excited heavy baryons in the relativistic quark–diquark picture

The mass spectra of the excited heavy baryons consisting of two light (u,d,s$u,d,s$) and one heavy (c,b$c,b$) quarks are calculated in the heavy-quark–light-diquark approximation within the constituent quark model. The light quarks, forming the diquark, and the light diquark in the baryon are treated completely relativistically. The expansion in v/c$v/c$ up to the second order is used only for the heavy (b and c) quarks. The internal structure of the diquark is taken into account by inserting the diquark–gluon interaction form factor. An overall good agreement of the obtained predictions with available experimental data is found.     

Fermion family recurrences in the Dyson–Schwinger formalism

We study the multiple solutions of the truncated propagator Dyson–Schwinger equation for a simple fermion theory with Yukawa coupling to a scalar field. Upon increasing the coupling constant g, other parameters being fixed, more than one non-perturbative solution breaking chiral symmetry becomes possible and we find these numerically. These “recurrences” appear as a mechanism to generate different fermion generations as quanta of the same fundamental field in an interacting field theory, without assuming any composite structure. The number of recurrences or flavors is reduced to the question of the value of the Yukawa coupling, and it has no special profound significance in the standard model. The resulting mass function can have one or more nodes and the measurement that potentially detects them can be thought of as a collider-based test of the virtual dispersion relation for the charged lepton member of each family. This requires the three independent measurements of the charged lepton’s energy, three-momentum and off-shellness. We illustrate how this can be achieved for the (more difficult) case of the tau lepton. PACS 12.15.Ff; 11.30.Rd     

Calculation of open p-shell atoms in the algebraic approach of the Hartree–Fock method

Highly precise calculations of analytical Hartree–Fock orbitals and energies have been performed within the limits of the Roothaan–Hartree–Fock atomic theory (Roothaan–Bagus method) for all open p-shell atoms of the Periodic Table. They were calculated in an algebraic approach using Slater-type atomic orbitals (AOs) as basis functions. Nonlinear parameters (orbital exponents) of AOs were optimized with exceptional accuracy by second-order methods. As a result, it was possible to satisfy exactly the virial relation (10^–14–10^–17) with calculated atomic term energies being close to the Hartree–Fock limit.     

Nonstationary Theory of Perturbations for Open-Shell Atoms in the Hartree–Fock Approximation

For a multielectron open-shell system exposed to an external time-dependent perturbation, the Hartree–Fock nonstationary equations are obtained in terms of density operators. Using them as a basis, equations of nonstationary coupled perturbation theory are suggested in orbital representation within the framework of the two-operator variant of the Roothaan method for an open shell. The perturbation theory corrections to the orbitals have been found in the form of expansions in unperturbed orbitals which are assumed to be calculated in the LCAO approximation in the basis of Slater-type atomic orbitals. The dynamic polarizability of open-shell atoms of substances from Li to F and Sc has been calculated as an even-power series of the frequency of incident radiation.     

Study of Octupole Deformation of Radium Isotopes in the Hartree–Fock–Bogoliubov Approximation with Skyrme Forces

Physics of Atomic Nuclei - The change in the octupole deformation of nuclei in the chain of even–even radium isotopes is studied on the basis of the Hartree–Fock–Bogoliubov method...     

Peculiarities in the Formation of X-Ray Fluxes by Waveguide–Resonators of Different Construction

The phenomenon of total external reflection (TER) of quasi-monochromatic X-ray radiation fluxes on a material interface and the effect of waveguide–resonator propagation of these fluxes in nanosize extended slit clearance, as well as a device operating on the basis of this effect—a planar X-ray waveguide–resonator—are briefly described. Experimental data on the formation of an X-ray flux by a composite X-ray waveguide–resonator are presented, and a model describing the decrease in the angular divergence of the formed flux without a decrease in the integral intensity is proposed. The model is based on the conception of partial angular tunneling of the radiation flux in the gap between two consequently mounted and mutually adjusted waveguide–resonators; the tunneling is implemented due to the interaction between interference fields of standing X-ray waves excited by the radiation transported by the slit clearance of these waveguide–resonators.     

Optical Properties of SiO2 Films Obtained by the Sol‐Gel Method in the Presence of Modifiers of Different Nature

The degrees of hydrolysis of tetraethoxysilane (TEOS) in filmforming compositions containing hydrolysis catalysts and modifiers of different nature have been determined. The TEOS hydrolysis depth has been estimated by the IR spectroscopic method. It is shown that the optical absorption of films depends on the amount of the immobilized indicator and the initial conditions for film formation.     

Analytical Solution of the Klein–Fock–Gordon Equation for the Rosen–Morse Potential

Russian Physics Journal - With the help of a successful scheme for overcoming difficulties arising for l ≠ 0 in the centrifugal part of the Rosen–Morse potential with bound states, a...     

Effects of Radiative Corrections in the Drell–Yan Process at Ultrahigh Dilepton Invariant Masses

Physics of Atomic Nuclei - One-loop electroweak and QCD radiative corrections in the Drell–Yan process at ultrahigh energies and dilepton invariant masses are calculated. The refactoring of...     

Systems of Linear Dyson–Schwinger Equations

Mathematical Physics, Analysis and Geometry - In this study, we consider a quantum waveguide with random boundary conditions . Precisely we consider Laplace operator restricted to a two dimensional...     

On the Goos–Hänchen Effect in the Case of Excitation of Surface Waves in the Kretschmann Scheme

Optics and Spectroscopy - A theoretical method for investigating reflection of a finite-aperture plane light beam from a flat-layered structure in the Kretschmann scheme is considered. The...     

Solving the Dyson–Schwinger equation around its first singularities in the Borel plane

The Dyson–Schwinger equation of the massless Wess–Zumino model is written as an equation over the anomalous dimension of the theory. Its asymptotic behavior is derived and the procedure to compute the perturbations of this asymptotic behavior is detailed. This procedure uses ill-defined objects. To solve this, the Dyson–Schwinger equation is rewritten for the Borel plane. It is shown that the illdefined procedure in the physical plane can be applied in the Borel plane. Other results obtained in the Borel plane are stated and the proof for one result is described.