Direct solution of integration-by-parts systems

Systems of integration-by-parts identities play an important role in simplifying the higher-loop Feynman integrals that arise in quantum field theory. Solving these systems is equivalent to reducing integrals containing numerator products of irreducible invariants to a small set of master integrals....

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Bibliographic Details
Published in:Physical review. D 2018-07, Vol.98 (2), Article 025008
Main Author: Kosower, David A.
Format: Article
Language:English
Subjects:
Direct reduction
Field theory
High Energy Physics - Phenomenology
Integrals
Invariants
Mathematical analysis
Physics
Quantum field theory
Quantum theory
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Summary:Systems of integration-by-parts identities play an important role in simplifying the higher-loop Feynman integrals that arise in quantum field theory. Solving these systems is equivalent to reducing integrals containing numerator products of irreducible invariants to a small set of master integrals. We present a new approach to solving these systems that finds direct reduction equations for numerator terms of a given Feynman integral. As a particular example of its power, we show how to obtain reduction equations for arbitrary powers of irreducible invariants, along with their solutions.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.98.025008