Related papers: Computer algebra calculations in supersymmetric el…
This article reports on some recent progresses in Bessel moments, which represent a class of Feynman diagrams in 2-dimensional quantum field theory. Many challenging mathematical problems on these Bessel moments have been formulated as a…
It is known that every irreducible unitary representation of positive energy of the Poincar\'e group can be realized as a subspace of tensor fields on Minkowski spacetime subjected to suitable partial differential equations. We first…
It is shown how the geometrical splitting of N-point Feynman diagrams can be used to simplify the parametric integrals and reduce the number of variables in the occurring functions. As an example, a calculation of the…
A new method of divergence subtraction in Feynman parametric integrals is presented. The method is suitable for calculating the lepton anomalous magnetic moments (AMM) in quantum electrodynamics (QED). The subtraction procedure eliminates…
We derive exact, convergent representations of multiloop sunset Feynman integrals in two dimensions for arbitrary mass configurations and all loop orders valid for large Euclidean momentum. The integrals are expressed as sums of symmetric…
This paper introduces a new approach for the computation of electromagnetic field derivatives, up to any order, with respect to the material and geometric parameters of a given geometry, in a single Finite-Difference Time-Domain (FDTD)…
In this work we launch a systematic theory of superconformal blocks for four-point functions of arbitrary supermultiplets. Our results apply to a large class of superconformal field theories including 4-dimensional models with any number…
We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…
A numerical program is presented which facilitates the computation of the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such a task…
The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This…
We describe an efficient practical procedure for enumerating and regrouping vacuum Feynman graphs of a given order in perturbation theory. The method is based on a combination of Schwinger-Dyson equations and the two-particle-irreducible…
The Feynman diagram generator FeynArts and the computer algebra program FormCalc allow for an automatic computation of 2->2 and 2->3 scattering processes in High Energy Physics. We have extended this package by four new kinematical routines…
We develop a generating-function formulation for the symbolic reduction of multi-loop Feynman integrals. In this framework, integration-by-parts identities are rewritten as differential equations for sector-wise generating functions, so the…
The aim of XLOOPS is to calculate one-particle irreducible Feynman diagrams with one or two closed loops for arbitrary processes in the Standard model of particles and related theories. Up to now this aim is realized for all one-loop…
We present a general method for incorporating an external electromagnetic field into descriptions of few-body systems whose strong interactions are described by integral equations. In particular, we address the case where the integral…
We review different approaches to the graphical generation of the tadpole-free Feynman diagrams of the self-energy and the one-particle irreducible four-point function. These are needed for calculating the critical exponents of the…
A geometrical approach to the calculation of N-point Feynman diagrams is reviewed. It is shown that the geometrical splitting yields useful connections between Feynman integrals with different momenta and masses. It is demonstrated how…
A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…
In this work we present the computer algebra package HarmonicSums and its theoretical background for the manipulation of harmonic sums and some related quantities as for example Euler-Zagier sums and harmonic polylogarithms. Harmonic sums…
We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…