Related papers: Excursions into FeynArts and FormCalc
Feynman rules for the Standard Model including non-linear gauges are derived and implemented in the FeynArts package. The calculations using FeynArts with the new rules show that tree-level amplitudes are gauge invariant and that…
Feature requests are proposed by users to request new features or enhancements of existing features of software products, which represent users' wishes and demands. Satisfying users' demands can benefit the product from both competitiveness…
Type qualifiers offer a lightweight mechanism for enriching existing type systems to enforce additional, desirable, program invariants. They do so by offering a restricted but effective form of subtyping. While the theory of type qualifiers…
The intention of these notes is to give a mathematical account of how I believe students could be taught to think about functional programming languages and to explain how such languages work.
Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic:…
Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the…
We present a new Mathematica package that provides a platform to perform multi-loop computations. ANATAR integrates several existing tools designed for higher-order computations. In particular, it uses QGRAF to generate Feynman diagrams and…
When a new programming language appears, the syntax and intended behaviour of its programs need to be specified. The behaviour of each language construct can be concisely specified by translating it to fundamental constructs (funcons),…
xloops is a program package that calculates Feynman diagrams by using computer algebra systems. In this paper it is shown which problems to be solved by computer algebra arise during such calculations, and how this problems are handled in…
This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is…
Software frequently converts data from one representation to another and vice versa. Naively specifying both conversion directions separately is error prone and introduces conceptual duplication. Instead, bidirectional programming…
This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of particle interactions…
This article introduces the Mathematica package \emph{HEPMath} which provides a number of utilities and algorithms for High Energy Physics computations in Mathematica. Its functionality is similar to packages like FormCalc or FeynCalc, but…
By leveraging quantum-mechanical properties like superposition, entanglement, and interference, quantum computing (QC) offers promising solutions for problems that classical computing has not been able to solve efficiently, such as drug…
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future…
This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…
Understanding astrophysical and cosmological processes can be challenging due to their complexity and lack of intuitive analogies. To address this, we present \texttt{AstronomyCalc}, a Python package specifically designed to aid…
Developing and maintaining software commonly requires (1) adding new data type constructors to existing applications, but also (2) adding new functions that work on existing data. Most programming languages have native support for defining…
The discrete Fourier transform and the FFT algorithm are extended from the circle to continuous graphs with equal edge lengths.
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.