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

A bstract 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 instances a canonical basis can be chosen, which drastically simplifies the solution of the di...

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Published inThe journal of high energy physics Vol. 2017; no. 4; pp. 1 - 43
Main Author Meyer, Christoph
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2017
Springer Nature B.V
SpringerOpen
Subjects
Algorithms
Canonical forms
Classical and Quantum Gravitation
Differential equations
Elementary Particles
Field theory
High energy physics
Integrals
Mathematical analysis
Mathematical models
Physics
Physics and Astronomy
QCD Phenomenology
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Regulators
Relativity Theory
String Theory
Transformations
Transformations (mathematics)
QCD Phenomenology
Online AccessGet full text
ISSN1029-8479
1126-6708
1127-2236
1029-8479
DOI10.1007/JHEP04(2017)006

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Abstract A bstract 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 instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
AbstractList 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 instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
A bstract 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 instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
Abstract 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 instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
ArticleNumber 6
Author Meyer, Christoph
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  organization: Institut für Physik, Humboldt-Universität zu Berlin
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Snippet A bstract The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum...
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...
Abstract The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum...
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SubjectTerms Algorithms
Canonical forms
Classical and Quantum Gravitation
Differential equations
Elementary Particles
Field theory
High energy physics
Integrals
Mathematical analysis
Mathematical models
Physics
Physics and Astronomy
QCD Phenomenology
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Regulators
Relativity Theory
String Theory
Transformations
Transformations (mathematics)
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Title Transforming differential equations of multi-loop Feynman integrals into canonical form
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