Finding linear dependencies in integration-by-parts equations: A Monte Carlo approach

@article{Kant2013FindingLD,
  title={Finding linear dependencies in integration-by-parts equations: A Monte Carlo approach},
  author={Philipp Kant},
  journal={ArXiv},
  year={2013},
  volume={abs/1309.7287}
}
  • P. Kant
  • Published 27 September 2013
  • Computer Science
  • ArXiv
View PDF on arXiv
24 Citations
Background Citations
4
Methods Citations
6

Figures from this paper

24 Citations

A novel approach to integration by parts reduction

Algorithmic transformation of multi-loop Feynman integrals to a canonical basis

The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the…

Transforming differential equations of multi-loop Feynman integrals into canonical form

  • C. Meyer
  • Mathematics
    Journal of High Energy Physics
  • 2017
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many…

Transforming differential equations of multi-loop Feynman integrals into canonical form

A bstractThe method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in…

Reduction of Feynman integrals in the parametric representation

  • Wen Chen
  • Physics
    Journal of High Energy Physics
  • 2020
In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum…

Reduction of Feynman integrals in the parametric representation

  • Wen Chen
  • Physics
    Journal of High Energy Physics
  • 2020
In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum…

Symmetries of Feynman integrals and the Integration By Parts method

  • B. Kol
  • Mathematics, Physics
  • 2015
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…

Kira - A Feynman integral reduction program

  • Philipp MaierhöferJohann UsovitschP. Uwer
  • Computer Science
    Comput. Phys. Commun.
  • 2018

Results and techniques for higher order calculations within the gradient-flow formalism

A bstractWe describe in detail the implementation of a systematic perturbative approach to observables in the QCD gradient-flow formalism. This includes a collection of all relevant Feynman rules of…

Fully massive vacuum integrals at 5 loops

Massive vacuum integrals with a single mass scale are a class of Feynman integrals that appear in many precision calculations within the Standard Model of particle physics and have been calculated to…

29 References

Automatic integral reduction for higher order perturbative calculations

This paper implements the algorithm for the reduction of large systems of integrals to master integrals in MAPLE and develops two new features which keep the size of intermediate expressions relatively small throughout the calculation.

HIGH-PRECISION CALCULATION OF MULTILOOP FEYNMAN INTEGRALS BY DIFFERENCE EQUATIONS

Integration by parts: The algorithm to calculate β-functions in 4 loops

Algorithm FIRE—Feynman Integral REduction

The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases…

Differential Equations for Two-Loop Four-Point Functions

Recurrence relations for three-loop prototypes of bubble diagrams with a mass

Critical points and number of master integrals

A bstractWe consider the question about the number of master integrals for a multiloop Feynman diagram. We show that, for a given set of denominators, this number is totally determined by the…

FIRE4, LiteRed and accompanying tools to solve integration by parts relations

MATAD: a program package for the computation of MAssive TADpoles

The Exact Solution of Systems of Linear Equations with Polynomial Coefficients

An algorithm for computing exactly a general solution to a system of linear equations with coefficients that are polynomials over the integers by applying interpolation and the Chinese Remainder Theorem is presented.