相关论文: The Method of Arbitrarily Large Moments to Calcula…

The large moment method can be used to compute a large number of moments of physical quantities that are described by coupled systems of linear differential equations. Besides these systems the algorithm requires a certain number of initial…

We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically…

Single-scale quantities, like the QCD anomalous dimensions and Wilson coefficients, obey difference equations. Therefore their analytic form can be determined from a finite number of moments. We demonstrate this in an explicit calculation…

Single scale Feynman integrals in quantum field theories obey difference or differential equations with respect to their discrete parameter $N$ or continuous parameter $x$. The analysis of these equations reveals to which order they…

We present a method for symbolic calculation of Feynman amplitudes for processes involving both massless and massive fermions. With this approach fermion strings in a specific amplitude can be easily evaluated and expressed as basic Lorentz…

We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…

In this paper, we propose a new method for evaluating scalar one-loop Feynman integrals in generalized D-dimension. The calculations play an important building block for two-loop and higher-loop corrections to the processes at future…

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…

A new powerful method to calculate Feynman diagrams is proposed. It consists in setting up a Taylor series expansion in the external momenta squared (in general multivariable). The Taylor coefficients are obtained from the original diagram…

We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…

We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle…

The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try…

We discuss some of the problems that may occur in the calculation of complicated Feynman diagrams. These include the group independent evaluation of color factors, and the summation techniques that are needed for the expansion of diagrams…

In a recent paper \cite{ft} a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original…

An overview is presented on the current status of main mathematical computation methods for the multi-loop corrections to single scale observables in quantum field theory and the associated mathematical number and function spaces and…

In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast…

In this paper we describe a method of calculation of master integrals based on the solution of systems of difference equations in one variable. Various explicit examples are given, as well as the generalization to arbitrary diagrams.

Single scale quantities, as anomalous dimensions and hard scattering cross sections, in renormalizable Quantum Field Theories are found to obey difference equations of finite order in Mellin space. It is often easier to calculate fixed…

Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…

This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…