Related papers: Iterated Resolvent Function for the Ladder Bethe-S…
We present the results of a covariant constituent quark model, based on the Bethe-Salpeter equation, where confinement is implemented by a string like linear potential explaining the Regge trajectories. An instanton induced quark force…
The Green's functions for the Laplace equation respectively satisfying the Dirichlet and Neumann boundary conditions on the upper side of an infinite plane with a circular hole are introduced and constructed. These functions enables…
Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three dimensional scattering integral equations satisfying constraints of relativistic…
By introducing multipe-site correlation functions, we propose a hierarchical Green function approach, and apply it to study the characteristic properties of a 2D square lattice Hubbard model by solving the equation of motions of a…
The Green's function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of Green's function impedes the research of…
In this series of lectures we present the universal method based on the use of the functional integrals to derive the bound state equations for different two-body systems in elementary particle physics as well as in condensed matter theory:…
Starting from linear equations for the complex scalar field, the two- and three-point Green's functions are obtained in the infrared approximation. We show that the infrared singularity factorizes in the vertex function as in spinorial QED,…
We investigate and solve a special class of integrals involving associated Legendre functions, which can be regarded as generalized Mehler-Fock transformations. Some of the integrals appear naturally when dealing with the heat or resolvent…
We present useful connections between the finite difference and the finite element methods for a model boundary value problem. We start from the observation that, in the finite element context, the interpolant of the solution in one…
This article is the second in a series of two papers concerning the mathematical study of a boundary integral equation of the second kind that describes the interaction of $N$ dielectric spherical particles undergoing mutual polarisation.…
The Bethe-Salpeter equation for three bosons with zero-range interaction is solved for the first time. For comparison the light-front equation is also solved. The input is the two-body scattering length and the outputs are the three-body…
Since the breakthrough of twistronics a plethora of topological phenomena in two dimensions has appeared, specially relating topology and electronic correlations. These systems can be typically analyzed in terms of lattice models of…
Through this article we will use a notation \begin{equation}\label{alfaLap} T_{\alpha}u(x)=(1-|x|^2)\Delta u(x)+2 \alpha \langle x,\nabla u(x)\rangle + (n-2-\alpha) \alpha u(x). \end{equation} Here, $|x|<1$ and $\alpha>-1$. Also, for…
We present a calculation of the spectral properties of a single charge doped at a Cu($3d$) site of the Cu-F plane in KCuF$_{3}$. The problem is treated by generating the equations of motion for the Green's function by means of subsequent…
By either performing a Taylor expansion or making a polynomial approximation, the Bethe equation for charged particle stopping power in matter can be integrated analytically to obtain the range of charged particles in the continuous…
We solve the Bethe-Salpeter equation in order to calculate the spectrum of pseudoscalar, vector and scalar meson bound states for light as well as heavy quarks, extending our previous calculation of pseudoscalar mesons. The fermion…
We present a new method for solving the two-body Bethe-Salpeter equation in Minkowski space. It is based on the Nakanishi integral representation of the Bethe-Salpeter amplitude and on subsequent projection of the equation on the…
The imaginary-time Green's function is a building block of various numerical methods for correlated electron systems. Recently, it was shown that a model-independent compact orthogonal representation of the Green's function can be…
A Ward-Takahashi identity preserving Bethe-Salpeter kernel can always be calculated explicitly from a dressed-quark-gluon vertex whose diagrammatic content is enumerable. We illustrate that fact using a vertex obtained via the complete…
In the Light-Front Dynamics, the wave function equations and their numerical solutions, for two fermion bound systems, are presented. Analytical expressions for the ladder one-boson exchange interaction kernels corresponding to scalar,…