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REVIEW 5 major objections 4 minor 64 references

Quantum Field Theory Between Rigor and Pragmatism

T0 review · 5 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper argues that the long-standing divide between pragmatic and axiomatic quantum field theory should be understood through a realism quotient, and that beyond-the-Standard-Model progress requires the two programs to converge.

desk verdict A clear, honest synthesis of convergent realism and effective realism in QFT, but the realism quotient is defined so that its historical rise cannot fail, and the convergence recommendation rests on an asserted MUH premise. read the letter →

arxiv 2505.15577 v1 pith:L36XZCIJ submitted 2025-05-21 physics.hist-ph

Johannes Branahl This is my paper · ORCID
classification physics.hist-ph
keywords scientificrealisminstrumentalismquantumfieldtheoryaxiomaticbeyondtheStandardModelempiricaladequacyquotientmathematicaluniversehypothesis
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that the persistent split in quantum field theory—between the empirically triumphant but mathematically inconsistent conventional program and the mathematically rigorous but empirically silent axiomatic program—is best read through a single heuristic device called the realism quotient: the share of a theory's mathematical structures that are treated as real features of the world rather than mere tools for prediction. Reconstructed historically, that quotient rises steadily as experimental resolution improves, with each new theory keeping its realist elements and shedding its instrumental ones. Extrapolated forward, the same curve says that neither the conventional nor the axiomatic program is adequate on its own for physics beyond the Standard Model. The central normative claim is that the two programs must move toward each other—conventional QFT needs more consistency, axiomatic QFT more empirical flexibility—to reach the balance the current experimental era requires.

What carries the argument

The central object is the realism quotient R = (number of realistic mathematical structures)/(number of all mathematical structures), used as a heuristic ordering device rather than a measurable number. It does two jobs: retrospectively it labels the historical evolution of QFT as a sequence of theories with increasing R, where the 'white zone' marks the balance needed for empirical adequacy at a given experimental resolution; normatively it classifies theories as 'just-in-time' (R ≈ Rea), 'delayed workaround' (R < Rea), or 'premature wundertuete' (R > Rea), with historical examples from weak-interaction theory, the quark model, a unified field theory, and noncommutative geometry illustrating each category.

What would settle it

A clean test would be a mathematically consistent four-dimensional QFT that reproduces the Standard Model's predictions and then disagrees with conventional QFT at some energy; if experiment followed the inconsistent theory, the assumption that consistency tracks truth would be refuted, while agreement with the consistent theory would support the paper's realism quotient.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is a descriptive reconstruction plus a normative recommendation. The history of modern foundational physics can be rationally reconstructed as a rising realism quotient R, defined as the ratio of realistic to total mathematical structures in a theory, and this reconstruction supports a normative conclusion. Conventional QFT succeeds because it has historically stayed close to the required balance for each era's precision, but it now risks falling below that balance as beyond-the-Standard-Model theories carry its pragmatic compromises to energy scales a dozen orders of magnitude beyond the reach of current accelerators. Axiomatic QFT stands above the balance, consistent but empirically disconnected; its realism quotient is assumed higher because mathematical consistency is taken to be closer to truth than inconsistency. The paper therefore recommends that conventional QFT integrate more consistency-oriented methods and axiomatic QFT soften its axioms, so that future beyond-the-Standard-Model physics works inside the 'white zone' of empirical adequacy on the way toward the limit R → 1, a theory of everything.

Load-bearing premise

The load-bearing premise is that mathematical consistency is closer to truth than pragmatic but inconsistent models—the paper states this explicitly—so if the universe is not a mathematical structure, or if inconsistent mathematics can still track real structure, the direction of the realism quotient and the recommendation to favor axiomatic QFT collapse.

Editorial extensions

If this is right

  • If the realism quotient is the right lens, the beyond-the-Standard-Model crisis is not only experimental but structural, because carrying the Standard Model's instrumental compromises into new theories keeps R below the level that the next experimental era demands.
  • Axiomatic QFT should deliberately soften its axioms to make room for empirically testable four-dimensional models, and conventional QFT should adopt some of its consistency standards, so the two programs can merge into something like the unified QFT program of the early 1950s.
  • The model implies that 'surplus structure' in an idealistically motivated theory is not always a vice: the quark model's unobservable fractional-charge entities later became real, while a unified field theory stayed empirically sterile, so the same category can lead to two very different fates.
  • In the limit, a successful fundamental theory would have R = 1 and satisfy the stated theory-of-everything criteria: non-perturbative, unified, singular, internally consistent, and level-comprehensive.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial extension: the realism quotient is explicitly not measurable, so its predictive value will stand or fall on whether an independent ordering of theories by weight of realist structures tracks experimental resolution; that ordering could in principle be tested on historical cases beyond the four given.
  • Editorial extension: the same convergence argument could be applied to the measurement problem or to quantum gravity, which the paper brackets out; there the realist-structure side is even less settled, since no consistent quantum-gravitational structure is agreed on yet.
  • Editorial extension: the model suggests a concrete search heuristic for beyond-the-Standard-Model model-builders—prefer a new theory whose core mathematical objects are inherited from the Standard Model but whose ad hoc parameters are eliminated, since that is exactly the signature of an increasing realism quotient.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 4 minor

Summary. The paper introduces a 'realism quotient' R, defined as the number of realistic mathematical structures divided by the total number of mathematical structures in a theory, and uses it to model the history of 20th-century foundational physics as a process of increasing realism driven by increasing experimental resolution. It argues that conventional QFT (CQFT) has remained below the 'white zone' of empirical adequacy since the Standard Model, while axiomatic QFT (AxQFT) hovers above it, and it recommends that the two programs converge in order to make progress in BSM physics. The historical reconstruction is illustrated by four examples: Fermi's weak-interaction theory, Gell-Mann's Eightfold Way, Heisenberg's world formula, and Connes' noncommutative Standard Model. The normative conclusion is explicitly linked to the Mathematical Universe Hypothesis (MUH), which the paper endorses as a premise.

Significance. If the realism quotient could be given an independent and measurable or at least ordinal content, the paper would offer a valuable new lens on the Fraser-Wallace debate and on the crisis in BSM physics. Its strengths include a transparent statement of its heuristic limits (footnote 8), an explicit engagement with recent literature on QFT realism, and a clear taxonomy of theory dynamics through the categories of 'just-in-time', 'delayed workaround', and 'premature wundertuete'. As it stands, however, the central descriptive claim is illustrated rather than tested, and the normative recommendation is conditional on an asserted metaphysical premise. The paper is therefore more persuasive as a proposal for a conceptual framework than as a demonstration of the conclusions it draws from that framework.

major comments (5)
  1. [Sec. 4.1, Eq. (1) and footnote 8] The paper defines R as a quotient of counts of mathematical structures, but it also concedes in footnote 8 that 'Numerical values of R can hardly be specified in principle' and that 'even the unique countability of these elements may be doubted.' This is not a minor caveat: the normative claims — that R_BSM < Rea, that AxQFT lies above the white zone, and that the two programs must converge — all presuppose that comparisons of R can be made. Without a counting procedure or an independent ordinal criterion, the placement of CQFT and AxQFT in Fig. 1 is assigned ex post, and the central normative extrapolation rests on an unmeasurable quantity. The paper should provide at least a qualitative ordering criterion that can be applied without knowing the answer in advance.
  2. [Sec. 4.1, paragraph beginning 'Once again: the assumption'] The paper states: 'the assumption that AxQFT has a higher realism quotient is based on the hypothesis that mathematical consistency is in any case closer to truth than pragmatic, but inconsistent models like CQFT.' This premise is asserted, not defended. MUH is a contested metaphysical thesis; if an inconsistent theory can nevertheless track real structure, or if the universe is not a mathematical structure in the sense required by MUH, then the direction of the realism quotient and the recommendation to favor AxQFT lose their basis. The paper should either defend this premise or explicitly reformulate the normative conclusion as conditional on MUH and identify what would count as evidence against that conditional.
  3. [Sec. 4.1, response to Laudan] The paper defends its increasing-R historical thesis by claiming that 'the incommensurability of current theories to predecessor theories is nothing but an increase in the realism quotient R in the sense that realist elements are, by definition, incommensurable with some previously utilized instrumental elements.' This makes the descriptive retrospection unfalsifiable: because discarded structures are by definition labeled instrumental, any sequence of theory changes can be redescribed as R-increasing, and no historical case can count against the trend. An independent criterion for non-instrumental status — one that does not simply coincide with survival — is needed.
  4. [Sec. 4.2, historical examples] The four historical examples are selected to fit the proposed categories, but the paper provides no selection protocol and no discussion of potentially disconfirming cases. For a claim that 'the history of modern foundational physics can be modeled as a process in which theories evolve with a steadily increasing ratio of realist to instrumentalist mathematical elements,' a systematic survey or at least an explicit rule for choosing examples is required. As presented, the examples illustrate the model rather than test it, so they cannot bear the weight of the descriptive retrospection.
  5. [Sec. 4.1 and Sec. 4.3, 'same building blocks' claim] The paper asserts that lower-dimensional AxQFT models will provide 'the fundamental mathematical building blocks and thus the ontological foundation of future QFTs' in four dimensions, calling this 'the well-founded hope of AxQFT.' This projection is load-bearing: it underwrites the claim that AxQFT has a higher realism quotient and that convergence is advisable. However, no argument is given for why structures that arise in soluble toy models should survive in a future empirically adequate four-dimensional theory. This should be stated as a conjecture or supported with examples of structural continuity across dimensions, not assumed as a basis for the normative conclusion.
minor comments (4)
  1. [Throughout] There are several typographical errors: 'inavoidable' (p. 3), 'reconstrution' (p. 3), 'situtation' (p. 6), and 'mdoel' (p. 16) should be corrected.
  2. [Sec. 4.1] Rivat is cited as 'Rivat (2020)' in the text, but the corresponding reference is listed as Rivat (2021); please make the citation consistent with the bibliography.
  3. [Sec. 3] The experimental and theoretical values for the electron magnetic moment are written with German decimal commas ('gex. = 2,00231930436256(35)'), which is inconsistent with the English-language text and may confuse readers; use decimal points.
  4. [Fig. 1 and Fig. 2] The figures are explicitly described as created in Microsoft PowerPoint and are schematic. The paper would be easier to assess if the figures were accompanied by a table listing each historical example, its assigned category, and the evidence for that assignment, rather than relying on the visual placements alone.

Circularity Check

2 steps flagged · score 5.0 of 10

The realism quotient R is defined so that discarded structures count as instrumental, making the historical increase in R a definitional consequence rather than a derived result; the AxQFT-higher-R claim likewise reduces to the asserted consistency-is-truth premise.

  1. self definitional [Section 4.1, paragraph responding to Laudan's incommensurability critique]
    "However, the incommensurability of current theories to predecessor theories is nothing but an increase in the realism quotient R in the sense that realist elements are, by definition, incommensurable with some previously utilized instrumental elements that are not compatible with the mathematical structures of reality but were compatible with the limited degree of experimental precision."

    R is defined as the fraction of 'realistic mathematical structures' among all structures, and the realistic/instrumental label is assigned by survival and disposability: elements 'likely to survive the evolution of theories' are realistic, while 'subsequent historical disposability' marks elements as instrumental. The response to Laudan then declares that any incommensurable theory change is 'nothing but an increase in R', because the discarded elements were 'by definition' instrumental. This makes the historical trend 'R increases' unfalsifiable: every replacement of a predecessor theory is redescribed as an increase in R, regardless of its content.

  2. self definitional [Section 4.1, paragraph beginning 'Once again: the assumption that AxQFT has a higher realism quotient']
    "Once again: the assumption that AxQFT has a higher realism quotient is based on the hypothesis that mathematical consistency is in any case closer to truth than pragmatic, but inconsistent models like CQFT."

    This sentence presents the central ranking of AxQFT above CQFT as an 'assumption' and justifies it by equating mathematical consistency with closeness to truth. Under the MUH framework adopted in Chapter 2, realistic structures are those that correspond to the mathematical structure of reality, so consistency is treated as the criterion for realism. The conclusion 'AxQFT has a higher realism quotient' is therefore not derived from an independent measurement of R; it is the same claim restated as a premise: consistent structures are more realistic.

full rationale

The paper is a philosophy-of-physics proposal, not an empirical prediction, and it does not rely on self-citation or imported uniqueness theorems. The circularity is internal to the realism quotient model. The historical claim that R increases is made true by stipulation: structures that survive theory change are called 'realistic' and structures that are discarded are called 'instrumental', and incommensurability is then declared to be 'nothing but an increase in R'. Because the paper concedes that R cannot be numerically specified, the upward trajectory in Fig. 1 is not a measured trend but a labeling artifact. The normative ranking of AxQFT over CQFT similarly depends on asserting that mathematical consistency is closer to truth, which, given the MUH-based definition of realism, makes the higher-R claim a restatement of its own premise. The paper's explicit caveat that R is a heuristic reduces the severity, and the general recommendation for convergence between rigor and pragmatism has independent philosophical motivation. Nevertheless, the central load-bearing derivation from historical development to the normative prospection reduces to definitional moves, giving partial circularity with a score of 5.

Assumptions & free parameters 0 free parameters · 3 assumptions · 1 invented entities

No numerical parameters are fitted; the realism quotient R is deliberately unquantified. The model depends on philosophical axioms rather than empirical parameters.

assumptions (3)
  • domain assumption The physical universe is a mathematical structure (Tegmark's MUH), so inconsistent mathematical frameworks cannot both be real.
    Adopted in Chapter 2 as the basis for equating realism with mathematical consistency; this contested premise is not proven in the paper.
  • domain assumption Mathematical consistency is in any case closer to truth than pragmatic but inconsistent models.
    Stated in Sec. 4.1 as the hypothesis supporting the claim that AxQFT has a higher realism quotient than CQFT.
  • ad hoc to paper Each improved theory of foundational physics contains more realist elements than its predecessor.
    This monotonicity is built into the model's definition of R (Sec. 4.1) rather than derived from independent evidence.
invented entities (1)
  • Realism quotient R
    purpose: Heuristic metric for the share of realistic mathematical structures in a theory; used to locate theories relative to a required balance Rea and to justify the convergence recommendation.
    The paper states numeric values of R can hardly be specified in principle (Sec. 4.1), so R is a qualitative diagrammatic device without an external falsifiable handle.

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Cite this review

Pith. "Pith review of Quantum Field Theory Between Rigor and Pragmatism." pith.science (2026). https://pith.science/paper/L36XZCIJ

@misc{pith2026250515577,
  author       = {Pith},
  title        = {Pith review of: Quantum Field Theory Between Rigor and Pragmatism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L36XZCIJ}},
  note         = {Machine review of arXiv:2505.15577}
}
read the original abstract

Quantum Field Theory (QFT), the foundational framework of particle physics, has long existed in a state of tension between empirical success and mathematical rigor. Conventional QFT (CQFT), which underpins the Standard Model, offers unparalleled predictive accuracy but relies on inconsistent and ad hoc methods. In contrast, axiomatic QFT (AxQFT) aspires to a consistent, mathematically rigorous foundation, yet lacks empirical applicability. This paper introduces the heuristic vehicle of a realism quotient to model and navigate this tension, framing it as a dynamic balance between realism and instrumentalism in the mathematical structures of physical theories. By reconstructing the historical development of QFT and extrapolating its trajectory, the paper offers both a descriptive account of theoretical progress and a normative proposal: that CQFT and AxQFT must converge to address selected challenges of physics beyond the Standard Model. The model also contributes to broader debates in scientific realism, offering a structured framework for understanding the interplay between empirical adequacy and conceptual robustness and mathematical rigour in foundational physics.

Figures

Figures reproduced from arXiv: 2505.15577 by the authors.

Figure 1
Figure 1. [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Historical examples from particle physics illustrate the necessity of a balanced relationship between realistic and instrumental mathematical structures in fundamental physics, which must be regularly adjusted depending on experimental precision. Figure created with Microsoft Powerpoint 2023 Fermi’s Theory of Weak Interactions: Fermi’s theory of weak inter￾actions was an initial attempt to describe the weak nuclear … view at source ↗

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Works this paper leans on

64 extracted references · 52 canonical work pages

  1. [1]

    et al: Tenth-Order Electron Anomalous Magnetic Moment – Contribution of Diagrams without Closed Lepton Loops

    Aoyama, T. et al: Tenth-Order Electron Anomalous Magnetic Moment – Contribution of Diagrams without Closed Lepton Loops. Phys. Rev. D 91 (3): 033006 (2015).https: //doi.org/10.1103/PhysRevD.91.033006

    doi:10.1103/physrevd.91.033006 2015

  2. [2]

    Dissertation, Uni- versity of Western Ontario (2022)

    Athanasiou, D.: Effective Field Theories: A Philosophical Appraisal. Dissertation, Uni- versity of Western Ontario (2022)

    work page 2022

  3. [3]

    The Oxford Handbook of Topics in Philosophy (2014).https://doi.org/10.1093/oxfordhb/9780199935314.013.33

    Baker, D.: The Philosophy of Quantum Field Theory. The Oxford Handbook of Topics in Philosophy (2014).https://doi.org/10.1093/oxfordhb/9780199935314.013.33

    arXiv 2014

  4. [4]

    Bender, C.: Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70: 94 (2007). https://doi.org/10.1088/0034-4885/70/6/R03

    doi:10.1088/0034-4885/70/6/r03 2007

  5. [5]

    SpringerBriefs in History of Science and Technology

    Blum, A.: Heisenberg’s 1958 Weltformel and the Roots of Post-Empirical Physics.Con- tribution to the book series "SpringerBriefs in History of Science and Technology" (2019)

    work page 2019

  6. [6]

    https://doi.org/10.1023/A:1024139713910

    Cao, T.Y.:Structural Realism and the Interpretation of Quantum Field Theory.Synthese, 136(1): 3–2 (2003). https://doi.org/10.1023/A:1024139713910

    work page doi:10.1023/a:1024139713910 2003

  7. [7]

    In: Landry and Rickles: 187–206 (2012)

    Chakravartty, A.:Ontological Priority: The Conceptual Basis of Non-Eliminative, Ontic Structural Realism. In: Landry and Rickles: 187–206 (2012)

    work page 2012

  8. [8]

    Oxford University Press (2012)

    Close, F.: Neutrino. Oxford University Press (2012)

    work page 2012

Show all 64 references
  1. [9]

    Connes, A., Chamseddine, A.:Noncommutative Geometry as a Framework for Unifica- tion of all Fundamental Interactions including Gravity. Part I. Fortsch. Phys. 58: 553-600 (2010). https://doi.org/10.1002/prop.201000069

    2010 doi

  2. [10]

    JHEP 09: 104 (2012)

    Connes, A., Chamseddine, A.:Resilience of the Spectral Standard Model. JHEP 09: 104 (2012). https://doi.org/10.1007/JHEP09(2012)104

    2012 doi

  3. [11]

    In: Aguirre, A., B., Merali, Z

    Crowther, K.: When Do We Stop Digging? Conditions on a Fundamental Theory of Physics. In: Aguirre, A., B., Merali, Z. (Ed.), Springer Verlag (2019)

    2019

  4. [12]

    (Ed.): Why Trust a Theory? Epistemology of Modern Physics

    Dawid, R.:The Significance of Non-Empirical Confirmation in Fundamental Physics.In: Dardashti, R., Dawid, R., Thebault, K. (Ed.): Why Trust a Theory? Epistemology of Modern Physics. Cambridge University Press: 99-119 (2019)

    2019

  5. [13]

    Dougherty, J.:Effective and Selective Realisms.Preprint (2023)

    2023

  6. [14]

    Dyson, F.: The Radiation Theories of Tomonaga, Schwinger, and Feynman . Phys. Rev. 75(3): 486–502 (1949).https://doi.org/10.1103/PhysRev.75.486

    1949 doi

  7. [15]

    Dyson, F.:Divergence of perturbation theory in quantum electrodynamics. Phys. Rev. 85: 631–632 (1952). https://doi.org/10.1103/PhysRev.85.631

    1952 doi

  8. [16]

    Erkenntnis 64(3): 305-344 (2006)

    Earman, J., Fraser, D.: Haag’s Theorem and its Implications for the Foundations of Quantum Field Theory. Erkenntnis 64(3): 305-344 (2006). https://doi.org/10.1007/ s10670-005-5814-y

    2006

  9. [17]

    G.; Sukra, B

    Fan, X.; Myers, T. G.; Sukra, B. A. D.; Gabrielse, G.: Measurement of the Elec- tron Magnetic Moment. Phys. Rev. 130(7): 071801 (2023).https://doi.org/10.1103/ PhysRevLett.130.071801

    2023

  10. [18]

    La Ricerca Scientifica 2(12) (1933)

    Fermi, E.:Tentativo di una teoria dei raggi beta. La Ricerca Scientifica 2(12) (1933)

    1933

  11. [19]

    and Rejzner, K.:Algebraic Quantum Field Theory – an introduction

    Fewster, C. and Rejzner, K.:Algebraic Quantum Field Theory – an introduction. Preprint on arxiv:1904.04051 (2019).https://doi.org/10.48550/arXiv.1904.04051

    2019 doi arXiv

  12. [20]

    Feynman, R.: Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction. Phys. Rev. 80(3): 440–57 (1950). https://doi.org/10.1103/PhysRev.80. 440

    1950 doi

  13. [21]

    Studies in History and Philosophy of Science Part B, 39(4): 841–859 (2008).https://doi.org/10

    Fraser, D.: The fate of ’particles’ in quantum field theories with interactions. Studies in History and Philosophy of Science Part B, 39(4): 841–859 (2008).https://doi.org/10. 1016/j.shpsb.2008.05.003

    2008

  14. [22]

    Philosophy of Science 76(4): pp

    Fraser, D.:Quantum Field Theory: Underdetermination, Inconsistency, and Idealization. Philosophy of Science 76(4): pp. 536-567, The University of Chicago Press (2009).https: //doi.org/10.1086/649999

    2009 doi

  15. [23]

    In: Studies in History and Philosophy of Modern Physics 42(2): 126–135 (2011)

    Fraser, D.: How to Take Particle Physics Seriously: A Further Defence of Axiomatic Quantum Field Theory. In: Studies in History and Philosophy of Modern Physics 42(2): 126–135 (2011). https://doi.org/10.1016/j.shpsb.2011.02.002 26 J. Branahl

    2011 doi

  16. [24]

    PhD Thesis, University of Leeds (2016)

    Fraser, J.: What is Quantum Field Theory? Idealisation, Explanation and Realism in High Energy Physics. PhD Thesis, University of Leeds (2016)

    2016

  17. [25]

    Fraser, J.: The real problem with perturbative quantum field theory.The British Journal for the Philosophy of Science, 71(2): 391–413 (2020).h10.1093/bjps/axx042

    2020

  18. [26]

    California Institute of Technology Synchrotron Laboratory (1961)

    Gell-Mann, M.:The Eightfold Way: A Theory of Strong Interaction Symmetry. California Institute of Technology Synchrotron Laboratory (1961)

    1961

  19. [27]

    Physics Letters

    Gell-Mann, M.: A Schematic Model of Baryons and Mesons. Physics Letters. 8(3): 214–215 (1964). https://doi.org/10.1016/S0031-9163(64)92001-3

    1964 doi

  20. [28]

    Haag, R.: On quantum field theoriesMatematisk-fysiske Meddelelser 29:12 (1955)

    1955

  21. [29]

    Journal of Mathematical Physics, 5(7): 848–861 (1964).https://doi.org/10.1063/1.1704187

    Haag, R., Kastler, D.: An Algebraic Approach to Quantum Field Theory. Journal of Mathematical Physics, 5(7): 848–861 (1964).https://doi.org/10.1063/1.1704187

    1964 doi

  22. [30]

    Haag, R.: Local Quantum Physics: Fields, Particles, Algebras.Zweite Ausgabe, Berlin, Springer (1996)

    1996

  23. [31]

    In: Philosophy of Physics 134 (2007)

    Halvorson, H.: Algebraic Quantum Field Theory. In: Philosophy of Physics 134 (2007)

    2007

  24. [32]

    H 48(6) (2023)

    Harlander, R., Martinez, J., Schiemann, G.: The end of the particle era?Eur.Phys. H 48(6) (2023). https://doi.org/10.1140/epjh/s13129-023-00053-4

    2023 doi

  25. [33]

    Hartmann, S.: Effective field theories, reductionism, and scientific explanation.Studies in History and Philosophy of Modern Physics 32(2): 267–304 (2001).https://doi.org/ 10.1016/S1355-2198(01)00005-3

    2001 doi

  26. [34]

    Heisenberg, W.: Einführung in die einheitliche Feldtheorie der Elementarteilchen . S. Hirzel Verlag Stuttgart (1967)

    1967

  27. [35]

    Article in backreaction.blogspot.com (2020)

    Hossenfelder, S.:Physicists still lost in math. Article in backreaction.blogspot.com (2020)

    2020

  28. [36]

    Sitzungsber

    Kaluza, T.: Zum Unitätsproblem in der Physik. Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.): 966–972 (1921)

    1921

  29. [37]

    Kuhlmann, M.: Why conceptual rigour matters to philosophy: On the ontological sig- nificance of algebraic quantum field theory. Found. Phys. 40(9-10): 1625-1637 (2010). https://doi.org/10.1007/s10701-010-9474-7

    2010 doi

  30. [38]

    https://doi.org/10.1016/S0039-3681(98)80129-5

    Ladyman, J.:What Is Structural Realism?In: Studies in History and Philosophy of Sci- encePartA,29(3): 409–424(1998). https://doi.org/10.1016/S0039-3681(98)80129-5

    1998 doi

  31. [39]

    Landau, L., Abrikosov, A., Khalatnikov, I.M.:On the removal of infinities in quantum electrodynamics. Dokl. Akad. Nauk SSSR 95: 497–500 (1954)

    1954

  32. [40]

    Laporta, S.: High-precision calculation of the 4-loop contribution to the electron g-2 in QED. Phys. Lett. B772: 232–238, arXiv:1704.06996 (2017).https://doi.org/10.1016/ j.physletb.2017.06.056

    2017 arXiv

  33. [41]

    Philosophy of Science 48: 19-49, (1981)

    Laudan, L.: A Confutation of Convergent Realism. Philosophy of Science 48: 19-49, (1981)

    1981

  34. [42]

    https://doi.org/10.1007/s10670-005-3225-8

    Lyons, T.: Towards a Purely Axiological Scientific Realism.Erkenntnis, 63(2): 167–204 (2005). https://doi.org/10.1007/s10670-005-3225-8

    2005 doi

  35. [43]

    Maddy, P.:Naturalism in Mathematics.Oxford University Press, Oxford (1997)

    1997

  36. [44]

    In: Perspectives on Quantum Reality: Non-Relativistic, Relativistic, and Field-Theoretic, Dordrecht et al., Kluwer, 1–10 (1996)

    Malament, D.: In defense of dogma: Why there cannot be a relativistic quantum mech- anics of (localizable) particles. In: Perspectives on Quantum Reality: Non-Relativistic, Relativistic, and Field-Theoretic, Dordrecht et al., Kluwer, 1–10 (1996)

    1996

  37. [45]

    The British Journal for the Philosophy of Science 69(3) (2018)

    Miller, M.: Haag’s theorem, apparent inconsistency, and the empirical adequacy of quantum field theory. The British Journal for the Philosophy of Science 69(3) (2018). https://doi.org/10.1093/bjps/axw029

    2018 doi

  38. [46]

    Putnam, H.: Reason, Truth and History.Cambridge University Press (1981)

    1981

  39. [47]

    Nuovo Cimento, 22: 1051–1068 (1961)

    Reeh, H., Schlieder, S.:Bemerkungen zur Unitäräquivalenz von Lorentzinvarianten Feld- ern. Nuovo Cimento, 22: 1051–1068 (1961)

    1961

  40. [48]

    Rickles, D.: Mirror Symmetry and Other Miracles in Superstring Theory. Found. Phys. 43: 54–80 (2013).https://doi.org/10.1007/s10701-010-9504-5

    2013 doi

  41. [49]

    Available on arxiv no

    Rivasseau, V.: Why renormalizable noncommutative quantum field theories?. Available on arxiv no. 0711.1748 (2007).https://doi.org/10.48550/arXiv.0711.1748

    2007 doi arXiv

  42. [50]

    Synthese 198: 12107–12136 (2021)

    Rivat, S.: Effective Theories and Infinite Idealizations: A Challenge for Sci- entific Realism. Synthese 198: 12107–12136 (2021). https://doi.org/10.1007/ s11229-020-02852-4 Quantum Field Theory Between Rigor and Pragmatism 27

    2021

  43. [51]

    Ruetsche, L.: Renormalization group realism: The ascent of pessimism.Philosophy of Science, 85(5): 1176–1189 (2018).https://doi.org/10.1086/699719

    2018 doi

  44. [52]

    (eds.) Philosophical Foundations of Quantum Field Theory: 149–183

    Saunders, S.:The algebraic approach to quantum field theory.In: Brown, H.R., Harré, R. (eds.) Philosophical Foundations of Quantum Field Theory: 149–183. Clarendon, Oxford (1988)

    1988

  45. [53]

    Schwinger, J.:Quantum Electrodynamics. I. A Covariant Formulation. Phys Rev 74(10): 1439–61 (1948). https://doi.org/10.1103/PhysRev.74.1439

    1948 doi

  46. [54]

    https://plato

    Stanford Encyclopedia of Philosophy: Scientific Realism (2017). https://plato. stanford.edu/entries/scientific-realism/

    2017

  47. [55]

    Wightman:PCT, spin and statistics, and all that.Princeton Landmarks in Physics

    Streater, R., A. Wightman:PCT, spin and statistics, and all that.Princeton Landmarks in Physics. Princeton, NJ: Princeton University Press. Corrected third printing of the 1978 edition (2000)

    2000

  48. [56]

    Philosophy Compass 12(5): e12414 (2017).https://doi.org/10.1111/phc3.12414

    Swanson, S.:A philosopher’s guide to the foundations of quantum field theory. Philosophy Compass 12(5): e12414 (2017).https://doi.org/10.1111/phc3.12414

    2017 doi

  49. [57]

    Tegmark, M.: The mathematical universe. Found. Phys. 38: 101–150 (2008).https:// doi.org/10.1007/s10701-007-9186-9

    2008 doi

  50. [58]

    van Fraassen, B.:The Scientific Image.Oxford: Oxford University Press (1980)

    1980

  51. [59]

    The British Journal for the Philosophy of Science, 57(2): 275–307 (2006).https://doi.org/10.1093/bjps/axl002

    van Fraassen, B.: Structure: Its Shadow and Substance. The British Journal for the Philosophy of Science, 57(2): 275–307 (2006).https://doi.org/10.1093/bjps/axl002

    2006 doi

  52. [60]

    Synthese 151(1): 33–80 (2006).https://doi.org/10.1007/s11229-004-6248-9

    Wallace, D.:In Defence of Naiveté: The Conceptual Status of Lagrangian Quantum Field Theory. Synthese 151(1): 33–80 (2006).https://doi.org/10.1007/s11229-004-6248-9

    2006 doi

  53. [61]

    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42(2): 116-125 (2010).https://doi.org/10

    Wallace, D.: Taking particle physics seriously: A critique of the algebraic approach to quantum field theory. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42(2): 116-125 (2010).https://doi.org/10. 1016/j.shpsb.2010.12.001

    2010

  54. [62]

    Wightman, A.S.: Quantum field theory in terms of vacuum expectation values. Phys. Rev. 101: 860–866 (1956).https://doi.org/10.1103/PhysRev.101.860

    1956 doi

  55. [63]

    British Journal for the Philosophy of Science 70(1): 209-237 (2019).https://doi.org/10.1093/bjps/axx043

    Williams, P.: Scientific Realism Made Effective. British Journal for the Philosophy of Science 70(1): 209-237 (2019).https://doi.org/10.1093/bjps/axx043

    2019 doi

  56. [64]

    https://doi.org/10.1111/j.1746-8361.1989.tb00933.x 1Philosophisches Seminar der Universität Münster Domplatz 23, 48143 Münster, Germany e-mail: j_bran33@uni-muenster.de

    Worrall, J.: Structural Realism: The Best of Both Worlds?Dialectica 43(1–2): 99–124 (1989). https://doi.org/10.1111/j.1746-8361.1989.tb00933.x 1Philosophisches Seminar der Universität Münster Domplatz 23, 48143 Münster, Germany e-mail: j_bran33@uni-muenster.de

    1989

Pith tools

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