Related papers: Some Methods of Minimization of Calculations in Hi…
The article deals with a number of the existings variants of direct calculation of amplitudes of processes with polarized Dirac particles. It is shown, that all of them are special cases of one and the same mathematical scheme. The…
General scheme for covariant calculation of the amplitudes of processes with the polarized Dirac particles is considered. It is so concretized that the obtained expressions can be used for calculation of the amplitudes of processes with…
The various ways to reduce number of vectors describing condition of particles for high energy physics problems are presented. In particular decomposition of any vector with respect to the basis, consisting of any four linearly independent…
A covariant method is proposed for calculating the amplitudes of processes involving polarized spin 1/2 particles. It is suitable for calculating the interference terms in the cross sections of such processes. As an illustration,…
A selection of unfolding methods commonly used in High Energy Physics is compared. The methods discussed here are: bin-by-bin correction factors, matrix inversion, template fit, Tikhonov regularisation and two examples of iterative methods.…
Energy minimization methods are a classical tool in a multitude of computer vision applications. While they are interpretable and well-studied, their regularity assumptions are difficult to design by hand. Deep learning techniques on the…
The methods of reduced phase space quantization and Dirac quantization are examined in a simple gauge theory. A condition for the possible equivalence of the two methods is discussed.
We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solution is represented as a product of two matrices, and…
We present an alternative approach for calculating helicity amplitudes for processes involving both massless and massive fermions. With this method one can easily obtain covariant expressions for the helicity amplitudes. The final…
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the…
Many problems in science and engineering can be rigorously recast into minimizing a suitable energy functional. We have been developing efficient and flexible solution strategies to tackle various minimization problems by employing finite…
The usual method of solving the free particle Dirac equation results in the so called continuum energy solutions. Here, we take a different approach and find a set of solutions with quantized energies which are proportional to the total…
The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…
An approximate diagonalization method is proposed that combines exact diagonalization and perturbation expansion to calculate low energy eigenvalues and eigenfunctions of a Hamiltonian. The method involves deriving an effective Hamiltonian…
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,…
The reduced basis method is used to construct a "universal" basis of Dirac orbitals that may be applicable throughout the nuclear chart to calibrate covariant energy density functionals. Relative to our earlier work using the…
A diagrammatic technique is derived for calculating processes involving the production of large numbers of particles. As an example, the amplitude of three particles scattering into $n$ particles at the kinematical threshold in…
The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in detail.
A new method of calculation of amplitudes of different processes in quantum electrodynamics is proposed. The method does not use the Feynman technique of trace of product of matrices calculation. The method strongly simplifies calculation…