Feynman Diagrams: Modeling between Physics and Mathematics

Stöltzner, Michael

doi:10.1162/posc_a_00284

Cited by 9 publications

(9 citation statements)

References 20 publications

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“…6 As a result, the close relationship between experiment and theoretical calculations determined much of the dynamics of early postwar high-energy physics. 7 In fact, two essential calculations for the development and confirmation of QED at the lowest significant order were carried out before Feynman developed his diagrammatic method. They were related to the Lamb shift and the anomalous magnetic moment of the electron.…”

Section: The Emergence Of Computer-aided Feynman Diagram Calculationsmentioning

confidence: 99%

The development of computational methods for Feynman diagrams

Harlander,

Martinez

2024

EPJ H

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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.

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Section: The Emergence Of Computer-aided Feynman Diagram Calculationsmentioning

confidence: 99%

The development of computational methods for Feynman diagrams

Harlander,

Martinez

2024

EPJ H

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“…The various uses of Feynman diagrams in everyday and professional communication by physicists has been discussed by Kaiser (1993) and Stöltzner (2018), for example. In this respect, it is obviously crucial that they allow to convey a lot of information by simply drawing a few lines on a piece of paper or a blackboard.…”

Section: Feynman Diagrams In Present-day Calculationsmentioning

confidence: 99%

“…Their historical development and dissemination as well as their diverse fields of application (calculation, communication, education, intuition, etc. ) have been subject of study also in the reflective sciences (Brown 2018;Dorato and Rossanese 2018;Wüthrich 2018;Schweber 1994;Kaiser 1993;Wüthrich 2010;Stöltzner 2018). And their multifaceted forms have inspired physicists even in non-scientific aspects, as exemplified by the creative names that they have given to specific diagrams, some of which are shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Feynman diagrams

Harlander

2021

Synthese

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The way from the path integral to Feynman diagrams is sketched. The emphasis is put on the decrease of complexity in this process, from infinite-dimensional integrals down to the apparent simplicity of child’s play. On the other hand, also the subsequent increase in complexity when using Feynman diagrams to make realistic physical predictions is described, thus illustrating the dialectic between the simplicity and clarity of Feynman diagrams, and the complexity in their practical applications.

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“…But in the case of a quantum field and especially a superfluid BEC one might well push back against the claim that there are, in any meaningful sense, individual particles. The literature on this is vast and we will not dwell on it here [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. If it is correct that there are not in any meaningful sense individual particles in a superfluid BEC, it would be the case that phonons and particles are both ontologically independent of each other, and that neither of them exists everywhere in a SFDM-model that could describe our actual universe.…”

Section: Metaphysical and Formal Asymmetrymentioning

confidence: 99%

Cartography of the space of theories: an interpretational chart for fields that are both (dark) matter and spacetime

Martens¹,

Lehmkuhl²

2020

Preprint

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This paper pushes back against the Democritean-Newtonian tradition of assuming a strict conceptual dichotomy between spacetime and matter. Our approach proceeds via the more narrow distinction between modified gravity/spacetime (MG) and dark matter (DM). A prequel paper argued that the novel field Φ postulated by Berezhiani and Khoury's 'superfluid dark matter theory' is as much (dark) matter as anything could possibly be, but alsobelow the critical temperature for superfluidity-as much (of a modification of) spacetime as anything could possibly be. Here we introduce and critically evaluate three groups of interpretations that one should consider for such Janus-faced theories. The consubstantiality interpretation holds that Φ is both (dark) matter and a modification of spacetime, analogously to the sense in which Jesus (according to catholicism) is both human and god. The fundamendalist interpretations consider for each of these roles whether they are instantiated fundamentally or emergently. The breakdown interpretations focus on the question of whether Φ signals the breakdown, in some sense to be specified, of the MG-DM dichotomy and perhaps even the broader spacetimematter distinction. More generally, it is argued that hybrid theories urge a move towards a single space of theories, rather than two separate spaces of spacetime theories and matter theories, respectively.

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Feynman Diagrams: Modeling between Physics and Mathematics

Cited by 9 publications

References 20 publications

The development of computational methods for Feynman diagrams

The development of computational methods for Feynman diagrams

Feynman diagrams

Cartography of the space of theories: an interpretational chart for fields that are both (dark) matter and spacetime

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