Truncated Möbius inversions for partial sums over scattering diagrams

Determine whether partial sums over scattering diagrams in quantum field theory can be described and effectively approximated as truncated Möbius inversions relative to an appropriate mereology (for example, the partition lattice), and assess the practical usefulness of such truncated inversions for approximating scattering amplitudes.

Background

In the Discussion, the paper proposes transferring approximation schemes inspired by Möbius inversions across scientific domains. The cluster variation method in statistical physics can be viewed as a truncated Möbius inversion over subsets of lattice sites, and similar truncations have been suggested in chemistry for molecular properties.

Extending this idea to quantum field theory, the authors point out that scattering amplitudes are computed via sums over Feynman diagrams. They raise the question of whether partial sums over such diagrams could be fruitfully represented as truncated Möbius inversions, which would provide a principled mereological approximation framework for scattering processes.