Related papers: A Novel Approach in Solving the Spinor-Spinor Beth…
We numerically examine the exterior solution of spherically symmetric and static configuration in scalar-tensor theories by using the nonminimally coupled scalar field with zero potential as our sample model. Our main purpose in this work…
The mass spectrum of heavy pseudoscalar mesons, described as quark-antiquark bound systems, is considered within the Bethe-Salpeter formalism with momentum dependent masses of the constituents. This dependence is found by solving the…
The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with $\delta$-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering…
A scalar field method to obtain transverse solutions of the vector Laplace and Helmholtz equations in spherical coordinates for boundary-value problems with azimuthal symmetry is described. Neither scalar nor vector potentials are used.…
With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving…
By application of the 'geometric spectral inversion' technique, which we have recently generalized to accommodate also singular interaction potentials, we construct from spectral data emerging from the solution of the Minkowski-space…
We shortly review different methods to obtain the scattering solutions of the Bethe-Salpeter equation in Minkowski space. We emphasize the possibility to obtain the zero energy observables in terms of the Euclidean scattering amplitude.
The problem of calculating of the mass spectrum of the two-body Bethe-Salpeter equation is studied with no reduction to the three-dimensional ("quasipotential") equation. The method to find the ground state and excited states for a channel…
In this paper, we propose a horizontal type method of lines numerical scheme for the unsteady Euler-Bernoulli beam equation. The problem is initially reformulated as a first order system of initial value problems and a suitable one-step…
We consider Mellin-Barnes transform of triangle ladder-like scalar diagram in d=4 dimensions. It is shown how the multi-fold MB transform of the momentum integral corresponding to an arbitrary number of rungs is reduced to the two-fold MB…
We developed the formal connection of the field theoretical Bethe-Salpeter equation including the ladder approximation with its representation on the light-front for a bosonic model. We use the light-front Green's function for the…
The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by…
In this paper we propose a new numerical method for solving stochastic differential equations (SDEs). As an application of this method we propose an explicit numerical scheme for a super linear SDE for which the usual Euler scheme diverges.
The Bethe-Salpeter equation provides the most widely used technique to extract bound states and resonances in a relativistic Quantum Field Theory. Nevertheless a thorough discussion how to identify its solutions with physical states is…
Recently developed methods allowing to find the solutions of the Bethe-Salpeter equations in Minkowski space, both for the bound and scattering states, are reviewed. For the bound states, one obtains the bound state mass and the…
Scalar, vector and tensor harmonics on the three-sphere were introduced originally to facilitate the study of various problems in gravitational physics. These harmonics are defined as eigenfunctions of the covariant Laplace operator which…
In this paper we consider the single patch pseudo-spectral scheme for tensorial and spinorial evolution problems on the 2-sphere presented in [3,4] which is based on the spin-weighted spherical harmonics transform. We apply and extend this…
The relation between solutions to Helmholtz's equation on the sphere $S^{n-1}$ and the $[{\gr sl}(2)]^n$ Gaudin spin chain is clarified. The joint eigenfuctions of the Laplacian and a complete set of commuting second order operators…
Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through use of integer spin weighted spherical harmonics we present a method which allows for the implementation of arbitrary…
Using the complete orthonormal sets of radial parts of nonrelativitistic exponential type orbitals (2,1, 0, 1, 2, ...) and spinor type tensor spherical harmonics of rank s the new formulae for the 2(2s+1)-component relativistic spinors…