Integral reduction in loop-by-loop Baikov representation

Feynman loop integrals represent a fundamental topic in the study of scattering amplitudes within quantum field theory. In this dissertation we present an approach for the analysis of multi-loop Feynman integrals properties, employing syzygy equations within the loop-by-loop Baikov representation. By identifying propagators as integration variables and performing the parametrization iteratively, this framework generates a more compact system of Integration-by-Parts identities, an essential tool to perform the so called integral reduction of an integral family. Furthermore, our analysis includes the derivation of the differential equations for both families using polynomial decomposition techniques, which further optimize the reduction process. The results are successfully validated by applying our algorithm to two two-loop cases: the massless box-triangle and double-box families.