Related papers: Some recent results on evaluating Feynman integral…
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…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
Integration By Parts (IBP) is an important method for computing Feynman integrals. This work describes a formulation of the theory involving a set of differential equations in parameter space, and especially the definition and study of an…
Integer relation algorithms can convert numerical results for Feynman integrals to exact evaluations, when one has reason to suspect the existence of reductions to linear combinations of a basis, with rational or algebraic coefficients.…
A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for the evaluation of Feynman diagrams. The operational rules are described and the method is…
By introducing an auxiliary parameter, we find a new representation for Feynman integrals, which defines a Feynman integral by analytical continuation of a series containing only vacuum integrals. The new representation therefore…
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 address the problem of evaluation of multiloop Feynman integrals by means of their Mellin-Barnes representation. After a brief overview of available capabilities though open source toolkits and their application in various circumstances,…
Mellin-Barnes (MB) representations have become a widely used tool for the evaluation of Feynman loop integrals appearing in perturbative calculations of quantum field theory. Some of the MB integrals may be solved analytically in closed…
Mellin-Barnes (MB) integrals appear in various branches of physics and mathematics and are, in particular, used as a standard tool for evaluating multi-loop, multi-scale Feynman integrals both analytically and numerically. Recent geometric…
I present an algorithm based on sector decomposition and Mellin-Barnes techniques to power expand Feynman integrals. The coefficients of this expansion are given in terms of finite integrals that can be calculated numerically. I show in an…
Feynman integrals may be represented by the Mathematica packages AMBRE and MB as multiple Mellin-Barnes integrals. With the Mathematica package MBsums these Mellin-Barnes integrals are transformed into multiple sums.
An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…
This course on Feynman integrals starts from the basics, requiring only knowledge from special relativity and undergraduate mathematics. Topics from quantum field theory and advanced mathematics are introduced as they are needed. The course…
The Feynman integral can be seen as an attempt to relate, under certain circumstances, the quantum-information-theoretic separateness of mutually unbiased bases to causal proximity of the measuring processes.
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…
A number of irreducible master integrals for L-loop sunrise-type and bubble Feynman diagrams with generic values of masses and external momenta are explicitly evaluated via Mellin-Barnes representation.
We present short review of two methods for obtaining functional equations for Feynman integrals. Application of these methods for finding functional equations for one- and two- loop integrals is described in detail. It is shown that with…
The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear…
We discuss the determination of the infrared singularities of massive one-loop 5-point functions with Mellin-Barnes (MB) representations. Massless internal lines may lead to poles in the $\eps$ expansion of the Feynman diagram, while…