arXiv subjects

B. A. Fayzullaev

Publications and source records attributed to B. A. Fayzullaev.

5 recordsLinked to original sources

arXiv2024

New method for the solution of the two-body Dirac equation for the positronium bound states

A new theoretical method is developed to solve the two-body bound-state Dirac equation for positronium. Only Coulomb potential was included in the Dirac Hamiltonian. It is shown that the two-body Dirac Hamiltonian can be written in the Hermitian matrix form of the 4$\times$4 size and diagonalized in the momentum-state representation. Numerical results for the energy spectrum of the para- and ortho-positronium ground states performed within the variational method using the harmonic oscillator basis functions are in good agreement with a high-precision finite-element method of T.C. Scott et al. After the Fourier transformation into the coordinate-state representation the bound state wave functions of the para-Ps and ortho-Ps do not contain any singularity at the origin in contrast to the method mentioned above. The weights of the large-small and small-large components of the ground state wave functions are estimated to be of order 10$^{-6}$, while the weight of the small-small component is of order 10$^{-12}$.

hep-ph↗

arXiv2020

Schwinger-Dyson type equations for some QFT models

The Schwinger-Dyson equations connecting free and full Green functions and vertex parts widely were used in QED for finding full Green functions under different conditions. Undoubtedly, the same approach should leads to derivation of many useful information about other models of QFT. In this work we present some technique based on variational equations for effective action to derive many different Schwinger-Dyson type equations in QFT models such as nonlinear sigma model and scalar field theory.

hep-th↗

arXiv2015

Effective action and vacuum expectations in nonlinear $σ$ model

The equations for effective action for nonlinear $σ$ model are derived using DeWitt method in two forms - for generator of vertex parts $Γ$ and for generator of weakly connected parts $W$. Loop-expansion solutions to these equations are found. It is shown that vacuum expectation values for various quantities including divergence of a Nöther current, trace of the energy-momentum tensor and so on, can be calculated by this method. Also it is shown that vacuum expectation to the sigma-field is determined by an explicit combination of tree Green function and classical solution. It is shown that the limit when coupling constant tends to zero is singular one.

hep-th↗

arXiv2005

Knot soliton in Weinberg-Salam model

We study numerically the topological knot solution suggested recently in the Weinberg-Salam model. Applying the SU(2) gauge invariant Abelian projection we demonstrate that the restricted part of the Weinberg-Salam Lagrangian containing the interaction of the neutral boson with the Higgs scalar can be reduced to the Ginzburg-Landau model with the hidden SU(2) symmetry. The energy of the knot composed from the neutral boson and Higgs field has been evaluated by using the variational method with a modified Ward ansatz. The obtained numerical value is 39 Tev which provides the upper bound on the electroweak knot energy.

hep-th↗

arXiv2004

The s-wave pi d scattering length from pi d atom using effective field theory

The pi- d atom strong energy-level shift in the 1s state is derived by using the effective field theory. Taking into account the large value of radius of pionic deuterium and short radius of strong interaction between pion and deuteron we have considered deuteron as particle described by vector field. Pion is described by scalar field. To obtain non-relativistic Hamiltonian for pi d system Foldy-Wouthuysen transformation has been derived for the vector field. The strong interaction between pion and deuteron has been taken at the zero-range approach. We have found the Deser type formula for relation between the strong energy-level shift and the s-wave pi d scattering length.

hep-ph↗