Related papers: On the phase-integral method for the radial Dirac …
An approximation method, namely, the Extended Wronskian Determinant Approach, is suggested to study the one-dimensional Dirac equation. An integral equation which can be solved by iterative procedure to find the wave functions is…
The two-body Dirac equation with general local potential is reduced to the pair of ordinary second-order differential equations for radial components of a wave function. The class of linear + Coulomb potentials with complicated spin-angular…
A generalized Dick model with a potential term is discussed. The solution originating from a static, pointlike, color source is found to have a confining part. The comparison with a wide spectrum of phenomenological quark-antiquark…
Exact solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic…
We apply the complex scaling method to the calculation of scattering phase shifts and extract the contributions of resonances in a phase shift and a cross section. The decomposition of the phase shift is shown to be useful to understand the…
The problem of evaluating potential integrals on planar triangular elements has been addressed using a polar coordinate decomposition. The resulting formulae are general, exact, easily implemented, and have only one special case, that of a…
We present a reduction procedure for gauge theories based on quotienting out the kernel of the presymplectic form in configuration-velocity space. Local expressions for a basis of this kernel are obtained using phase space procedures; the…
In the canonical approach to general relativity it is customary to parametrize the phase space by initial data on spacelike hypersurfaces. However, if one seeks a theory dealing with observations that can be made by a single localized…
In this paper we develop and demonstrate a method to obtain epsilon factorized differential equations for elliptic Feynman integrals. This method works by choosing an integral basis with the property that the period matrix obtained by…
The concept of nonlinear modes is useful for the dynamical characterization of nonlinear mechanical systems. While efficient and broadly applicable methods are now available for the computation of nonlinear modes, nonlinear modal testing is…
This paper is devoted to a study of relativistic eigenstates of Dirac particles which are simultaneously bound by a static Coulomb potential and added linear confining potentials. It has recently been shown that, despite the addition of…
Spectral properties and the confinement phenomenon for the coupling $H+V$ are studied, where $H=-i\alpha\cdot\nabla +m\beta$ is the free Dirac operator in $\mathcal{R}^3$ and $V$ is a measure-valued potential. The potentials $V$ under…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
This paper applies the phase-integral method to the stationary theory of alpha-decay. The rigorous form of the connection formulae, and their one-directional nature that was not widely known in the physical literature, are applied. The…
Advantageous numerical methods for solving the Dirac equations are derived. They are based on different stochastic optimization techniques, namely the Genetic algorithms, the Particle Swarm Optimization and the Simulated Annealing method,…
A model in which a Dirac particle in $\mathbb{R}^{3}$ is bound by $N\geqslant1$ spatially distributed zero-range potentials is presented. Interactions between the particle and the potentials are modeled by subjecting a particle's bispinor…
We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform…
We present a spectral method for one-sided linear fractional integral equations on a closed interval that achieves exponentially fast convergence for a variety of equations, including ones with irrational order, multiple fractional orders,…
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.