AMFlow: A Mathematica package for Feynman integrals computation via auxiliary mass flow
TLDR
AMFlow as mentioned in this paper is a Mathematica package to numerically compute dimensionally regularized Feynman integrals via the recently proposed auxiliary mass flow method, which can be obtained by constructing and solving differential systems with respect to this parameter, in an automatic way.About:
This article is published in Computer Physics Communications.The article was published on 2022-01-27 and is currently open access. It has received 65 citations till now. The article focuses on the topics: Computer science & Feynman diagram.read more
Citations
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Automatic computation of Feynman integrals containing linear propagators via auxiliary mass flow
Zhi-Feng Liu,Yan Ma +1 more
TL;DR: In this article , a recipe to systematically calculate Feynman integrals containing linear propagators using the auxiliary mass decomposition method was proposed, where the key of the recipe is to introduce a quadratic term for each linear propagator and then using differential equations to get rid of their effects.
Journal ArticleDOI
Determining Feynman Integrals with Only Input from Linear Algebra.
Zhi-Feng Liu,Yan Ma +1 more
TL;DR: In this paper, it was shown that all Feynman integrals (FIs) having any number of loops can be completely determined once linear relations between FIs are provided, and that FI computation is conceptually changed to a linear algebraic problem.
Journal ArticleDOI
Determining Feynman Integrals with Only Input from Linear Algebra
TL;DR: In this paper , it was shown that all Feynman integrals (FIs) having any number of loops can be completely determined once linear relations between FIs are provided, and that FI computation is conceptually changed to a linear algebraic problem.
References
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Journal ArticleDOI
Integration by parts: The algorithm to calculate β-functions in 4 loops
K.G. Chetyrkin,F.V. Tkachov +1 more
TL;DR: In this paper, it was proved that the counterterm for an arbitrary 4-loop Feynman diagram in an arbitrary model is calculable within the minimal subtraction scheme in terms of rational numbers and the Riemann ζ-function in a finite number of steps via a systematic "algebraic" procedure involving neither integration of elementary, special, or any other functions, nor expansions in and summation of infinite series of any kind.
Book
Asymptotic expansions for ordinary differential equations
TL;DR: Asymptotic expansions for ordinary differential equations as discussed by the authors, asymptotics expansions for ODEs, Asymptotically expansion for ordinary DDEs and their derivatives.
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High-precision calculation of multiloop feynman integrals by difference equations
TL;DR: Algorithms for the construction of the systems using integration-by-parts identities and methods of solutions by means of expansions in factorial series and Laplace transformation and procedures for generating and solving systems of differential equations in masses and momenta for master integrals are shown.
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Multiloop integrals in dimensional regularization made simple
TL;DR: It is argued that a good choice of basis for (multi)loop integrals can lead to significant simplifications of the differential equations, and criteria for finding an optimal basis are proposed.