Automating Renormalization of Quantum Field Theories

TL;DR

This paper discusses automated methods for renormalization in quantum field theories, focusing on symbolic computation techniques for multi-loop Feynman diagrams and comparing different computer algebra systems.

Contribution

It introduces automation of BPHZ renormalization using henges and sectors, and compares Maple and FORM for symbolic tensor and gamma-matrix manipulations.

Findings

Automated renormalization process using henges and sectors.

Comparison of Maple and FORM for symbolic computations.

Enhanced efficiency in multi-loop Feynman diagram evaluations.

Abstract

We give an overview of state-of-the-art multi-loop Feynman diagram computations, and explain how we use symbolic manipulation to generate renormalized integrals that are then evaluated numerically. We explain how we automate BPHZ renormalization using "henges" and "sectors", and give a brief description of the symbolic tensor and Dirac gamma-matrix manipulation that is required. We shall compare the use of general computer algebra systems such as Maple with domain-specific languages such as FORM, highlighting in particular memory management issues.