Theoretical analysis demonstrates direct reduction of integration-by-parts systems in Feynman integrals, highlighting a streamlined pathway for higher-loop quantum field theory calculations.
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.
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David A. Kosower (2018) studied this question.
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