FORM, Diagrams and Topologies

TL;DR

The work tackles automatic processing of vast numbers of 4-loop massless propagator diagrams by extending FORM-based tooling (Forcer) to optimize diagram insertion handling, topology detection, and reduction strategies. Key innovations include graph-automorphism driven pattern matching (id,all) for pruning subgraphs, a flexible topology-mapping workflow, and the id_ feature to tailor numerators for efficient reductions. These methods yield substantial performance gains, enabling scalable, high-precision multi-loop calculations and broader applicability to complex diagram families. Together, they advance automated diagram management, topology analysis, and reduction techniques in high-order quantum field theory computations.

Abstract

We discuss a number of FORM features that are essential in the automatic processing of very large numbers of diagrams as used in the Forcer program for 4-loop massless propagator diagrams. Most of these features are new.