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. I 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, I show how to obtain reduction equations for arbitrary powers of irreducible invariants, along with their solutions.