Related papers: Dirac: a command-line $\gamma$-matrix calculator
Fundamental solutions of Dirac type operators are introduced for a class of conformally flat manifolds. This class consists of manifolds obtained by factoring out the upper half-space of $\mathbb{R}^n$ by arithmetic subgroups of generalized…
The possibility of interaction between Maple and numeric compiled languages in performing extensive numeric calculations is exemplified by the Ndynamics package, a tool for studying the (chaotic) behavior of dynamical systems. Programming…
The paper proposes an algorithm for regularization of the self-energy expressions for a Dirac particle that meets the relativistic and gauge invariance requirements.
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional…
We review the enveloping algebra of the 10 dimensional chiral sigma matrices. To facilitate the computation of the product of several chiral sigma matrices we have developed a symbolic program. Using this program one can reduce the…
We present Version 8 of the Feynman-diagram calculator FormCalc. New features include in particular significantly improved algebraic simplification as well as vectorization of the generated code. The Cuba Library, used in FormCalc, features…
Mathematical justifications are given for several integral and series representations of the Dirac delta function which appear in the physics literature. These include integrals of products of Airy functions, and of Coulomb wave functions;…
In this article we report the release of a new program for calculating the emissivity of atomic transitions. The program, which can be obtained with its documentation from our website www.scienceware.net, passed various rigorous tests and…
Digital signal theory is an extension of the analysis of continuous signals. This extension is provided by discretization and sampling. The sampling of signals can be mathematically described by a series of Dirac impulses and is well known.…
General description of an on-line procedure of calibration for IGRT (Image Guided Radiotherapy) is given. The algorithm allows to improve targeting cancer by estimating its position in space and suggests appropriate correction of the…
Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The found solutions are expressed in terms of new complex…
Distributed quantum computing (DQC) is a promising proposal for overcoming the scalability challenges of quantum computing. However, the evaluation of DQC hardware and software is difficult due to the relative dearth of classical simulation…
We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.
A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.
A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show…
We discuss some linear algebra related to the Dirac matrix D of a finite simple graph G=(V,E).
Our computation effort is primarily concentrated on support of current and future measurements being carried out at various synchrotron radiation facilities around the globe, and photodissociation computations for astrophysical…
Development of computer technology in chemistry, bring many application of chemistry. Not only the application to visualize the structure of molecule but also to molecular dynamics simulation. One of them is Gromacs. Gromacs is an example…
The use of complexified quaternions and $i$-complex geometry in formulating the Dirac equation allows us to give interesting geometric interpretations hidden in the conventional matrix-based approach.
Chord diagrams and combinatorics of word algebras are used to model products of Dirac matrices, their traces, and contractions. A simple formula for the result of arbitrary contractions is derived, simplifying and extending an old…