Related papers: The Calculation of Matrix Elements in Relativistic…
We propose a new class of short matrix recurrences for the solution of nonsymmetric linear equations of the type $\mathbf{A}_1\mathbf{X}\mathbf{B}_1+\ldots+\mathbf{A}_p\mathbf{X}\mathbf{B}_p=CD^T$. These iterative methods combine local…
Neutral-meson mixing is loop suppressed in the Standard Model, leading to the possibility of enhanced sensitivity to new physics. The uncertainty in Standard Model predictions for $B$-meson oscillation frequencies is dominated by…
A peculiar representation of the Lorentz group is suggested as a starting point for a consistent approach to relativistic quantum theory.
The increasing use of multivariate methods, and in particular the Matrix Element Method (MEM), represents a revolution in experimental particle physics. With continued exponential growth in computing capabilities, the use of sophisticated…
Analytical periodic solutions for weakly Coupled Map Lattices are shown in an explicit form as well as in a recurrence relation. The results establish a link between a matricial representation and recurrence relations of the solutions.
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
A lattice quantum chromodynamics (LQCD) calculation of the nuclear matrix element relevant to the $nn\to ppee\overline{\nu}_e\overline{\nu}_e$ transition is described in detail, expanding on the results presented in Ref. [1]. This matrix…
I compare the matrix representation of the basic statements of Special Relativity with the conventional vector space representation. It is shown, that the matrix form reproduces all equations in a very concise and elegant form, namely:…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…
We use the recently calculated two--loop anomalous dimensions of current-current operators, QCD and electroweak penguin operators to construct the effective Hamiltonian for $\Delta S=1$ transitions beyond the leading logarithmic…
We study the effects of a barely perceivable violation of Lorentz invariance on results computed using a relativistic constituent quark model wave function. The model nucleon wave function of Gross {\it et al.} is constructed such thatthere…
Light-front current matrix elements for elastic scattering from hadrons with spin~1 or greater must satisfy a nontrivial constraint associated with the requirement of rotational covariance for the current operator. Using a model $\rho$…
We discuss the relationship between quaternion algebras and quadratic forms with a focus on computational aspects. Our basic motivating problem is to determine if a given algebra of rank 4 over a commutative ring R embeds in the 2x2-matrix…
The nuclear waste problem is one of the main interests of the rare earth and actinide elements chemistry. Studies of Actinide-containing compounds are at the frontier of the applications of current theoretical methods due to the need to…
We present in this report 1+1 dimensional nonlinear partial differential equation integrable through inverse scattering transform. The integrable system under consideration is a pseudo-Hermitian reduction of a matrix generalization of…
The Dirac equation for H$_2^+$ is solved numerically using an iterative method proposed by Kutzelnigg [Z. Phys. 11, 15 (1989]. The four-component wavefunction is expanded in a newly introduced kinetically balanced exponential basis set. The…
In this paper, we consider the one-dimensional semirelativistic Schr\"{o}dinger equation for a particle interacting with $N$ Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an $N \times…
We introduce a method for describing Riordan matrices via recurrence relations along their diagonals. This provides a new structural description that complements the classical row-wise and column-wise constructions via the A-sequence. As an…
There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a…
In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear…