Modern techniques of multiloop calculations
Roman N. Lee
TL;DR
The paper surveys advanced techniques for multiloop Feynman integral calculations, emphasizing automation and reduction via integration-by-parts and master integrals. It reviews parameterizations and algebraic approaches (including the Lee-Pomeransky representation and syzygy/Groebner-basis methods) to derive IBP relations directly in parametric form and to count master integrals. It also covers the differential equations method, notably epsilon-form simplifications, and dimensional recurrence relations (DRA) as complementary tools for solving master integrals across dimensions. Together, these methods aim to enable efficient, scalable computations of high-order loop corrections in quantum field theories.
Abstract
I present a few new and recent ideas of the multiloop calculations.