Related papers: Numerical computation of Fox functions
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.
The program package XLOOPS calculates massive one- and two-loop Feynman diagrams. It consists of five parts: i) a graphical user interface ii) routines for generating diagrams from particle input iii) procedures for calculating one-loop…
We discuss a progress in calculation of Feynman integrals which has been done with help of the Differential Equation Method and demonstrate the results for a class of two-point two-loop diagrams.
This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.
I discuss algorithms for the evaluation of Feynman integrals. These algorithms are based on Hopf algebras and evaluate the Feynman integral to (multiple) polylogarithms.
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…
We present a new computer program, $\texttt{feyntrop}$, which uses the tropical geometric approach to evaluate Feynman integrals numerically. In order to apply this approach in the physical regime, we introduce a new parametric…
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…
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…
In this work we report on a new version of FeynCalc, a Mathematica package widely used in the particle physics community for manipulating quantum field theoretical expressions and calculating Feynman diagrams. Highlights of the new version…
We survey and investigate some computational aspects of the Fourier-Mukai transform.
Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector…
This article presents two methods, in parallel, of solving more complex integrals, among which is the Poisson's integral, in order to emphasize the obvious advantages of a new method of integration, which uses the supermathematics circular…
The method for functional reduction of Feynman integrals, proposed by the author, is used to calculate one-loop integrals corresponding to diagrams with four external lines. The integrals that emerge from amplitudes for the scattering of…
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…
Special values of the Lommel functions allow the calculation of Fresnel like integrals. These closed form expressions along with their asymptotic values are reported.
We propose numerical integration methods for Choquet integrals where the capacities are given by distortion functions of an underlying probability measure. It relies on the explicit representation of the integrals for step functions and can…
Higher transcendental function occur frequently in the calculation of Feynman integrals in quantum field theory. Their expansion in a small parameter is a non-trivial task. We report on a computer program which allows the systematic…
A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.