Karla Weingarten
LMU Munich
Feynman diagrams are a method prominent in quantum field theory and, more specifically, effective field theories, where individual or subgroups of diagrams are frequently used to depict intricate particle interactions. Notably, the CMS Collaboration employed Feynman diagrams to illustrate Higgs particle decay channels [4]. Similarly, in quantum many-body physics, subgroups of ladder- like looking Feynman diagrams play a crucial role in the Hartree-Fock method for approximating quantum many-body systems’ ground state energies [1]. Hence, it seems apparent that physicists use Feynman diagrams to visualize the content of the debate, illustrate their arguments, and further the readers’ understanding of their paper. In other words, they use Feynman diagrams to represent the physics situation.
However, philosophers’ stances on Feynman diagrams appear to diverge from physicists’ dominant practice. They are often regarded as mathematical artefacts rather than faithful representations of physical reality due to their selective portrayal of possible ways for the interactions to take place and, in field theories, their explicit presentation of unobservable virtual particles. Feynman diagrams not only idealize by disregarding higher-order perturbative contributions but add structure to the model by depicting the interaction in one particular, distorting way. Only the incoming and outgoing particles are arguably represented accurately. For that reason, it has been previously contended that individual Feynman diagrams do not represent [2, 3].
To address this disparity between philosophy and physics practice, this talk proposes to conceptualize Feynman diagrams as models of particle interactions, modeling the elements (particles) of the physical situation with lines, its mechanisms (interactions) with vertices, and ensuring structural resemblance with the formalism through the Feynman rules. A model approach allows us to treat internal lines as model entities only, setting aside any realism concerns. Rather than considering Feynman diagrams to be instruments or fictions, this take emphasizes that they are a model of a target, in line with dominant physics practice.
Current approaches to representation require extensive target knowledge for constructing a model, where the connection is established via faithful resemblance and geared towards obtaining further target knowledge through substitute reasoning, disregarding other possible aims of science. Inspired by the case of Feynman diagrams, an alternative account of representation will be proposed, which is aimed at understanding: A model M accurately represents a target T iff M objectively provides understanding of T to a competent agent employing an appropriate interpretation. Understanding, together with an agent’s intention to represent a target with a model, is sufficient to establish the representational link between them.
While Feynman diagrams as models may not offer factual knowledge, they contribute to a deeper understanding of the target. Through the process of modeling, users can identify patterns and mechanisms and narrow down possible causal relations. Grasping these model behaviors facilitates target understanding. This goes beyond mere knowledge of possibilities of target behavior; it also allows the cognitive achievement of fundamentally comprehending a phenomenon as a whole, providing insights that can be embedded in broader knowledge of the scientific field, advancing the model user’s work.
In conclusion, reconceptualizing Feynman diagrams as models not only enhances our comprehension of their practical utility but also promises to enrich the discourse on scientific representation and understanding. This perspective invites broader implications for further modeling practices, particularly at the forefront of science, where knowledge might be out of reach.
References
[1] D. J. Broadhurst. ‘Summation of an infinite series of ladder diagrams’. In: Physics Letters B 307.1 (1993), pp. 132–139. issn: 0370-2693. doi: 10.1016/0370-2693(93)90202-S.
[2] Mauro Dorato and Emanuele Rossanese. ‘The Nature of Representation in Feynman Diagrams’. In: Perspectives on Science 26.4 (2018), pp. 443–458. issn: 1063-6145. doi: 10.1162/posc_ a_00282.
[3] Michael Stöltzner. ‘Feynman Diagrams: Modeling between Physics and Mathematics’. In: Perspectives on Science 26.4 (2018), pp. 482–500. issn: 1063-6145. doi: 10.1162/posc_a_ 00284.
[4] The CMS Collaboration. ‘Evidence for the 125 GeV Higgs boson decaying to a pair of leptons’. In: Journal of High Energy Physics 2014.5 (2013), pp. 587–609. issn: 1029-8479. doi: 10. 1007/JHEP05(2014)104.
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SOPhiA 2026 