The development of computational methods for Feynman diagrams

The European Physical Journal H, vol. 49

Abstract

Abstract Over the last 70 years, Feynman diagrams have played an essential role in the development of many theoretical predictions derived from the standard model Lagrangian. In fact, today they have become an essential and seemingly irreplaceable tool in quantum field theory calculations. In this article, we propose to explore the development of computational methods for Feynman diagrams with a special focus on their automation, drawing insights from both theoretical physics and the history of science. From the latter perspective, the article particularly investigates the emergence of computer algebraic programs, such as the pioneering , , and , designed to handle the intricate calculations associated with Feynman diagrams. This sheds light on the many challenges faced by physicists when working at higher orders in perturbation theory and reveal, as exemplified by the test of the validity of quantum electrodynamics at the turn of the 1960s and 1970s, the indispensable necessity of computer-assisted procedures. In the second part of the article, a comprehensive overview of the current state of the algorithmic evaluation of Feynman diagrams is presented from a theoretical point of view. It emphasizes the key algorithmic concepts employed in modern perturbative quantum field theory computations and discusses the achievements, ongoing challenges, and potential limitations encountered in the application of the Feynman diagrammatic method. Accordingly, we attribute the enduring significance of Feynman diagrams in contemporary physics to two main factors: the highly algorithmic framework developed by physicists to tackle these diagrams and the successful advancement of algebraic programs used to process the involved calculations associated with them.

Authors 2

1. Robert V. Harlander corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   TTK, RWTH Aachen University, Aachen, Germany

   RWTH Aachen - RWTH Aachen University = Rheinisch-Westfälische Technische Hochschule Aachen (RWTH Aachen – Templergraben 55 – 52062 Aachen (Hausanschrift) – 52056 Aachen (Postanschrift) – Deutschland - Germany)

2. Jean‐Philippe Martinez Aachen

   RWTH Aachen University · Technische Universität Berlin

   Affiliation as printed

   Institute of History and Philosophy of Science, Technology, and Literature, Technische Universität Berlin, Berlin, Germany

   TTK, RWTH Aachen University, Aachen, Germany

   RWTH Aachen - RWTH Aachen University = Rheinisch-Westfälische Technische Hochschule Aachen (RWTH Aachen – Templergraben 55 – 52062 Aachen (Hausanschrift) – 52056 Aachen (Postanschrift) – Deutschland - Germany)

   TUB - Technical University of Berlin / Technische Universität Berlin (Straße des 17. Juni 135 10623 Berlin - Germany)