Quantum seminar | 01 October 2025

The talk reviews methods for automating multiloop calculations in quantum field theory. We introduce the Nickel diagrammatic notation and present the Python packages built on it (GraphState, Graphine, GTopology), which enable efficient automation of diagram generation in arbitrary QFT models, as illustrated for the φ^n model and QED. The packages also implement basic diagram manipulations that are useful for automating renormalization via the Bogoliubov R-operation. Some techniques, including G-functions and IR rearrangement, that allow simplification of diagrammatic expressions prior to integration will be discussed. Finally, a concise review of modern methods for computing loop integrals, both numerical and analytical, will be given.

Main paper/arXiv, related to the seminar, and other references

L. Ts. Adzhemyan, D. A. Evdokimov, M. V. Kompaniets, Hyperlogarithms in the theory of turbulence of infinite dimension, Nuclear Physics B 1008, 116716 (2024)