Automating renormalization of quantum field theories

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 γ-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.

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INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Physics

Additional Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
      I.1.4 Applications

General Terms:
Algorithms, Languages

Keywords:
Feynman diagrams, quantum field theory, renormalization theory