How Do Feynman Diagrams Work?

Brown, James Robert

doi:10.1162/posc_a_00281

Cited by 10 publications

(4 citation statements)

References 21 publications

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“…The articles by James RobertBrown (2018) and TobiasFox (2008) are cases in point.2 SeeFeynman (1949, 772-773) for the physical interpretation briefly outlined above and its connection to the mathematical structures.…”

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confidence: 99%

“The language of Dirac’s theory of radiation”: the inception and initial reception of a tool for the quantum field theorist

Ehberger

2022

Arch. Hist. Exact Sci.

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In 1927, Paul Dirac first explicitly introduced the idea that electrodynamical processes can be evaluated by decomposing them into virtual (modern terminology), energy non-conserving subprocesses. This mode of reasoning structured a lot of the perturbative evaluations of quantum electrodynamics during the 1930s. Although the physical picture connected to Feynman diagrams is no longer based on energy non-conserving transitions but on off-shell particles, emission and absorption subprocesses still remain their fundamental constituents. This article will access the introduction and the initial reception of this picture of subsequent transitions (PST) by conceiving of concepts, models, and their representations as tools for the practitioners. I will argue for a multi-factorial explanation of Dirac’s initial, verbally explicit introduction: the mathematical representation he had developed was highly suggestive and already partly conceptualized; Dirac was philosophical flexible enough to talk about transitions when no actual transitions, according to the general interpretation of quantum mechanics of the time, occurred; and, importantly, Dirac eventually used the verbal exposition in the same paper in which he introduced it. The direct impact of PST on the conception of quantum electrodynamical processes will be exemplified by its reflection in diagrammatical representations. The study of the diverging ontological commitments towards PST immediately after its introduction opens up the prehistory of a philosophical debate that stretches out into the present: the dispute about the representational and ontological status of the physical picture connected to the evaluation of the perturbative series of QED and QFT.

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confidence: 99%

“The language of Dirac’s theory of radiation”: the inception and initial reception of a tool for the quantum field theorist

Ehberger

2022

Arch. Hist. Exact Sci.

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“…We provide here a mere sketch of the historical details with an eye to their philosophical interpretation as semiotic sign systems. Our central concern is to address the by now rather large philosophical literature promoting the view that FDs essentially function as models, or representations (Bacelar-Valente 2011;Meynell 2008Meynell , 2018Stölzner 2017;Wüthrich 2010;see also Harré 1988;Brown 2018). We agree with the representational emphasis and would like to provide some backup to these philosophical claims in the form of a grounding in Peircean semiotics.…”

Section: Diagrams Rules and Pragmaticismmentioning

confidence: 99%

“…In other words, FDs in addition represent processes that develop in spacetime. This dual aspect of FDs has sparked significant debate both in physics and in philosophy of physics (Brown 2018;Kaiser 2005;Meynell 2008Meynell , 2018Wüthrich 2010;Bacelar-Valente 2011;Stölzner 2017).…”

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confidence: 99%

Peirce’s Pragmatism, Semiotics, and Physical Representation

Sánchez-Ovcharov,

Suárez

2024

ejpap

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Charles Peirce is widely credited as the originator of semiotics, or the general theory of signs, and recognized as the founder of American pragmatism, albeit in that peculiar kind Peirce himself went on to distinguish as “pragmaticism.” The semiotic and pragmatist strands in Peirce’s thought come together in an appraisal of scientific diagrammatic representations. Peirce’s pragmatic maxim entails that the consequences of a sign inform our entire conception of the sign, while his most considered semiotic system entails that a complex sign partakes of iconic, indexical, and symbolic aspects. We illustrate Peirce’s insights by means of the celebrated Feynman Diagrams in Quantum Electrodynamics. We argue that Peirce’s late, post-1903, semiotics provides an adequate characterization of such “hypoicons,” and his pragmatic maxim explains how they can motivate and drive inquiry. We conclude that Peirce’s pragmatic approach to scientific diagrams remains a viable position that skillfully avoids dogmatic scientism and nihilistic skepticism alike.

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“…My account, however, generalizes without any modification to certain diagrams used in theoretical physics, such as Feynman diagrams. See (Brown, 2018) for a friendly introduction to the topic. 33 The process of explication can be, in fact, iterated multiple times (Dutilh Novaes and Reck, 2017).…”

Section: Diagrams: a Taxonomymentioning

confidence: 99%

What are mathematical diagrams?

Toffoli

2022

Synthese

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Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term "mathematical diagram" is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for a taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations (or both). I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain (away) certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading.

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How Do Feynman Diagrams Work?

Cited by 10 publications

References 21 publications

“The language of Dirac’s theory of radiation”: the inception and initial reception of a tool for the quantum field theorist

“The language of Dirac’s theory of radiation”: the inception and initial reception of a tool for the quantum field theorist

Peirce’s Pragmatism, Semiotics, and Physical Representation

What are mathematical diagrams?

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