Related papers: Dirac: a command-line $\gamma$-matrix calculator
In this paper we give simplified formulas for certain polynomials which arise in some new Titchmarsh-Weyl m-functions for the radial part of the separated Hydrogen atom on the half line and two independent programs for generating them using…
The overlap Dirac operator at nonzero quark chemical potential involves the computation of the sign function of a non-Hermitian matrix. In this talk we present an iterative method, first proposed by us in Ref. [1], which allows for an…
The model of a classical particle with the weak linear AAD potential is subjected to path integral quantization. The light cone constraints and peculiar properies of its internal variables permit to use in calculations commutative dynamics…
We present SuperTracer, a Mathematica package aimed at facilitating the functional matching procedure for generic UV models. This package automates the most tedious parts of one-loop functional matching computations. Namely, the…
Dirac particle dynamics is encoded as a unitary path summation rule and implemented on a qubit array, where the qubit array represents both spacetime and the fermions contained therein. The unitary path summation rule gives a quantum…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…
In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in $\mathbb{C}^n$, can be reduced to the computation of a family of constrained matrix representations of elements of the…
We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the…
The action of the overlap-Dirac operator on a vector is typically implemented in directly through a multi-shift conjugate gradient solver. The compute-time this takes to evaluate depends upon the condition number $\kappa$ of the matrix that…
It is demonstrated how the software system polymake can be used for computations in toric geometry. More precisely, counter-examples to conjectures related to A-determinants and defect polytopes are constructed.
A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions are developed to be…
The current version of 'carlomat', a program for automatic computation of the lowest order cross sections of multiparticle reactions, is described. The program can be used as the Monte Carlo generator of unweighted events as well.
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among…
A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…
We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$-complex geometry is overcome by a…
Zernike polynomials serve as an orthogonal basis on the unit disc, and have proven to be effective in optics simulations, astrophysics, and more recently in plasma simulations. Unlike Bessel functions, Zernike polynomials are inherently…
I present several tricks to help implement the overlap Dirac operator numerically.