Related papers: A note on recursive calculations of particular 9j …
In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…
Different relativistic quantum mechanics approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current…
Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
In this paper an exponential multiplicative formula for the R-matrix is provided for the twisted affine quantum algebras.
We discuss new ideas for consideration of loop diagrams and angular integrals in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of…
We calculate the orbital angular momentum of the `quark' in the scalar diquark model as well as that of the electron in QED (to order $\alpha$). We compare the orbital angular momentum obtained from the Jaffe-Manohar decomposition to that…
In this paper, the author present a reliable symbolic computational algorithm for inverting a general comrade matrix by using parallel computing along with recursion. The computational cost of our algorithm is O(n^2). The algorithm is…
In this paper, we study three applications of recursion to problems in coding and random permutations. First, we consider locally recoverable codes with partial locality and use recursion to estimate the minimum distance of such codes. Next…
Given standard angular momentum and boost matrices, the commutation rules for vector and momentum matrices are solved. The resulting matrix components are displayed as detailed functions of spin with factors such as the square root of…
We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb and long-range Ewald operators) are employed in quantum chemical calculations. We derive a…
Calculating the values of nuclear correlation functions is computationally intensive due to the fact that the number of terms in a nuclear wave function scales exponentially with atomic number. To speed up this computation, we represent a…
In this work, we describe examples for calculating the 1-D circular convolution of signals represented by 3-qubit superpositions. The case is considered, when the discrete Fourier transform of one of the signals is known and calculated in…
Yu and Littlejohn recently studied in arXiv:1104.1499 some asymptotics of Wigner symbols with some small and large angular momenta. They found that in this regime the essential information is captured by the geometry of a tetrahedron, and…
The computation of matrix functions is a well-studied problem. Of special importance are the exponential and the logarithm of a matrix, where the latter also raises existence and uniqueness questions. This is particularly relevant in the…
We apply the perturbative chiral quark model at one loop to calculate the strange form factors of the nucleon. A detailed numerical analysis of the strange magnetic moments and radii of the nucleon, and also the momentum dependence of the…
This paper is devoted to the analysis of the distribution of the total magnetic quantum number $M$ in a relativistic subshell with $N$ equivalent electrons of momentum $j$. This distribution is analyzed through its cumulants and through…
A modified Gibbs's rotation matrix is derived and the connection with the Euler angles, quaternions, and Cayley$-$Klein parameters is established. As particular cases, the Rodrigues and Gibbs parameterizations of the rotation are obtained.…
A new formulation is presented for a variational calculation of $N$-body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total…
We present a brief review of current methods for the calculation of multi-loop amplitudes including recent developments. As an example we present the calculation of the second moment of the heavy quark current correlator and the extraction…