Related papers: Dirac: a command-line $\gamma$-matrix calculator
It is proposed that the Dirac equation, as normally interpreted, incorporates intrinsic redundancies whose removal necessarily leads to an enormous gain in calculating power and physical interpretation. Streamlined versions of the Dirac…
This paper describes the VARTOOLS program, which is an open-source command-line utility, written in C, for analyzing astronomical time-series data, especially light curves. The program provides a general-purpose set of tools for processing…
The linearization of a quadratic form gives rise to a Clifford algebra structure, as seen in Dirac's factorization of the d'Alembert operator. A similar structure known as a generalized Clifford algebra arises from the continuation of this…
We study the discretization of (almost-)Dirac structures using the notion of retraction and discretization maps on manifolds. Additionally, we apply the proposed discretization techniques to obtain numerical integrators for port-Hamiltonian…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
Solving linear systems of polynomial equations is a ubiquitous problem in both mathematics and physics. The standard approach, Gaussian elimination, scales cubically with system size and often constitutes a computational bottleneck. The…
We present a computer program to calculate the quantised rotational and hyperfine energy levels of $^{1}\Sigma $ diatomic molecules in the presence of dc electric, dc magnetic, and off-resonant optical fields. Our program is applicable to…
This introductory presentation describes the Overlap Dirac Operator, why it could be useful in numerical QCD, and how it can be implemented.
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of…
We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code. Kranc can be used as a…
We present FeynCalc 9.3, a new stable version of a powerful and versatile Mathematica package for symbolic quantum field theory (QFT) calculations. Some interesting new features such as highly improved interoperability with other packages,…
The generalized Fermi-Dirac functions and their derivatives are important in evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized Fermi-Dirac…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
Presentation of set matrices and demonstration of their efficiency as a tool using the path/cycle problem.
Adinkras are graphical tools created for the study of representations in supersymmetry. Besides having inherent interest for physicists, adinkras offer many easy-to-state and accessible mathematical problems of algebraic, combinatorial, and…
We present a new software pipeline -- PyMorph -- for automated estimation of structural parameters of galaxies. Both parametric fits through a two dimensional bulge disk decomposition as well as structural parameter measurements like…
The paper provides an overview of core functionalities that digital democracy software needs to provide in order to support democratic deliberative processes at scale. Developing these functionalities poses novel computational challenges…
We obtain classes of two dimensional static Lorentzian manifolds, which through the supersymmetric formalism of quantum mechanics admit the exact solvability of Dirac equation on these curved backgrounds. Specially in the case of a modified…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator splitting decomposition technique that allows for a mapping of the…