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Quantum Field Theory: Underdetermination, Inconsistency, and Idealization

Published online by Cambridge University Press:  01 January 2022

Abstract

Quantum field theory (QFT) presents a genuine example of the underdetermination of theory by empirical evidence. There are variants of QFT—for example, the standard textbook formulation and the rigorous axiomatic formulation—that are empirically indistinguishable yet support different interpretations. This case is of particular interest to philosophers of physics because, before the philosophical work of interpreting QFT can proceed, the question of which variant should be subject to interpretation must be settled. New arguments are offered for basing the interpretation of QFT on a rigorous axiomatic variant of the theory. The pivotal considerations are the roles that consistency and idealization play in this case.

Type
Research Article
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

For helpful comments and suggestions, thanks to Laura Ruetsche, Gordon Belot, Nick Huggett, Dave Baker, Hilary Greaves, David Malament, David Wallace, Steve Weinstein, Michael Kiessling, Michael Fisher, James Mattingly, two anonymous referees, and especially John Earman. Thanks also to the audiences of the many talks in which versions of this material were presented. This research was partially supported by a doctoral fellowship from the Social Sciences and Humanities Research Council.

References

Baker, David J. (2009), “Against Field Interpretations of Quantum Field Theory”, Against Field Interpretations of Quantum Field Theory 60:585609.Google Scholar
Batterman, Robert (2005), “Critical Phenomena and Breaking Drops: Infinite Idealizations in Physics”, Studies in History and Philosophy of Science, Part B, Studies in History and Philosophy of Modern Physics 36:225244.CrossRefGoogle Scholar
Batterman, Robert (2009), “Idealization and Modeling”, Idealization and Modeling 169:427446.Google Scholar
Bender, Carl M. (2007), “Making Sense of Non-Hermitian Hamiltonians”, http://arxiv.org/abs/hep-th/0703096.Google Scholar
Buchholz, Detlev, and Summers, Stephen J. (2008), “Warped Convolutions: A Novel Tool in the Construction of Quantum Field Theories”, http://arxiv.org/abs/0806.0349.CrossRefGoogle Scholar
Callendar, Craig (2001), “Taking Thermodynamics Too Seriously”, Studies in History and Philosophy of Science, Part B, Studies in History and Philosophy of Modern Physics 32:539553.CrossRefGoogle Scholar
Cannon, John T., and Jaffe, Arthur M. (1970), “Lorentz Covariance of the λ(φ4)2 Quantum Field Theory”, Lorentz Covariance of the λ(φ4)2 Quantum Field Theory 17:261321.Google Scholar
Cao, Tian Yu (1997), Conceptual Developments of 20th Century Field Theories. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Coleman, Sidney, and Mandula, Jeffrey (1967), “All Possible Symmetries of the S-Matrix”, All Possible Symmetries of the S-Matrix 159:12511256.Google Scholar
da Costa, Newton, and French, Steven (2002), “Inconsistency in Science: A Partial Perspective”, in Meheus 2002, 105118.Google Scholar
Earman, John (2004), “Curie's Principle and Spontaneous Symmetry Breaking”, Curie's Principle and Spontaneous Symmetry Breaking 18:173198.Google Scholar
Earman, John, and Fraser, Doreen (2006), “Haag's Theorem and Its Implications for the Foundations of Quantum Field Theory”, Haag's Theorem and Its Implications for the Foundations of Quantum Field Theory 64:305344.Google Scholar
Emch, Gérard (1972), Algebraic Methods in Statistical Mechanics and Quantum Field Theory. New York: Wiley-Interscience.Google Scholar
Fraser, Doreen L. (2006), Haag's Theorem and the Interpretation of Quantum Field Theories with Interactions. PhD Dissertation. Pittsburgh: University of Pittsburgh. http://etd.library.pitt.edu/ETD/available/etd-07042006-134120/.Google Scholar
Fraser, Doreen L. (2008), “The Fate of ‘Particles’ in Quantum Field Theories with Interactions”, Studies in History and Philosophy of Science, Part B, Studies in History and Philosophy of Modern Physics 39:841859.CrossRefGoogle Scholar
Gårding, L., and Wightman, A. (1954), “Representations of the Commutation Relations”, Representations of the Commutation Relations 40:622626.Google ScholarPubMed
Glimm, James (1969), “Models for Quantum Field Theory”, in Jost, Res (ed.), Local Quantum Field Theory. New York: Academic Press, 97119.Google Scholar
Glimm, James, and Jaffe, Arthur (1968), “A λφ4 Quantum Field without Cutoffs. I”, Physical Review, Series 2, 176:19451951.CrossRefGoogle Scholar
Glimm, James, and Jaffe, Arthur (1970a), “The λ(Π4)2 Quantum Field Theory without Cutoffs. II. The Field Operators and the Approximate Vacuum”, Annals of Mathematics, Second Series, 91:362401.CrossRefGoogle Scholar
Glimm, James, and Jaffe, Arthur (1970b), “The λ(φ4)2 Quantum Field Theory without Cutoffs. III. The Physical Vacuum”, The λ(φ4)2 Quantum Field Theory without Cutoffs. III. The Physical Vacuum 125:203267.Google Scholar
Glimm, James, and Jaffe, Arthur (1971), “Quantum Field Theory Models”, in DeWitt, C. and Stora, R. (eds.), Statistical Mechanics and Quantum Field Theory. New York: Gordon and Breach, 1108.Google Scholar
Glimm, James, Jaffe, Arthur, and Spencer, Thomas (1974), “The Wightman Axioms and Particle Structure in the P(φ)2 Quantum Field Model”, Annals of Mathematics, Second Series, 100:585632.CrossRefGoogle Scholar
Haag, Rudolf (1955), “On Quantum Field Theories”, On Quantum Field Theories 29:137.Google Scholar
Haag, Rudolf (1996), Local Quantum Physics. 4th ed. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Haag, Rudolf, and Kastler, Daniel (1964), “An Algebraic Approach to Quantum Field Theory”, An Algebraic Approach to Quantum Field Theory 5:848861.Google Scholar
Haag, Rudolf, Łopuszański, Jan T., and Sohnius, Martin (1975), “All Possible Generators of Supersymmetries of the S-Matrix”, All Possible Generators of Supersymmetries of the S-Matrix 88:257274.Google Scholar
Hall, D., and Wightman, A. S. (1957), “A Theorem on Invariant Analytic Functions with Applications to Relativistic Quantum Field Theory”, A Theorem on Invariant Analytic Functions with Applications to Relativistic Quantum Field Theory 31:141.Google Scholar
Halvorson, Hans, and Müger, Michael (2007), “Algebraic Quantum Field Theory”, in Butterfield, Jeremy and Earman, John (eds.), Philosophy of Physics, Part A. Handbook of the Philosophy of Science. Boston: Elsevier, 731922.CrossRefGoogle Scholar
Huggett, Nick (2002), “Renormalization and the Disunity of Science”, in Kuhlmann, Meinard, Lyre, Holger, and Wayne, Andrew (eds.), Ontological Aspects of Quantum Field Theory. River Edge, NJ: World Scientific, 255277.CrossRefGoogle Scholar
Jaffe, Arthur (1999), “Where Does Quantum Field Theory Fit into the Big Picture?”, in Cao, Tian Yu (ed.), Conceptual Foundations of Quantum Field Theory. Cambridge: Cambridge University Press, 136147.CrossRefGoogle Scholar
Jost, Res (1965), The General Theory of Quantized Fields. Providence, RI: American Mathematical Society.Google Scholar
Keller, Joseph (1957), “On Solutions of Nonlinear Wave Equations”, On Solutions of Nonlinear Wave Equations 10:523530.Google Scholar
Kragh, Helge (1990), Dirac: A Scientific Biography. Cambridge: Cambridge University Press.Google Scholar
MacKinnon, Edward (2008), “The Standard Model as a Philosophical Challenge”, The Standard Model as a Philosophical Challenge 75:447457.Google Scholar
Meheus, Joke, ed. (2002), Inconsistency in Science. Boston: Kluwer.CrossRefGoogle Scholar
Mehra, Jagdish, and Rechenberg, Helmut (2001), The Historical Development of Quantum Theory. Vol. 5, Erwin Schroedinger and the Rise of Wave Mechanics—Early Response and Applications. New York: Springer.Google Scholar
Priest, Graham (2002), “Inconsistency and the Empirical Sciences”, in Meheus 2002, 119128.Google Scholar
Rivasseau, Vincent (2007), “Why Renormalizable Noncommutative Quantum Field Theories?”, http://arxiv.org/abs/0711.1748.Google Scholar
Ruetsche, Laura (2003), “A Matter of Degree: Putting Unitary Inequivalence to Work”, A Matter of Degree: Putting Unitary Inequivalence to Work 70:13291342.Google Scholar
Schweber, Silvan S. (1961), An Introduction to Relativistic Quantum Field Theory. Evanston, IL: Row, Peterson.Google Scholar
Schweber, Silvan S. (1994), QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Streater, Raymond F. (1988), “Why Should Anyone Want to Axiomatize Quantum Field Theory?”, in Brown, Harvey R. and Harré, Rom (eds.), Philosophical Foundations of Quantum Field Theory. New York: Oxford University Press, 136148.Google Scholar
Streater, Raymond F., and Wightman, Arthur S. (2000), PCT, Spin and Statistics, and All That. Princeton, NJ: Princeton University Press.Google Scholar
Teller, Paul (1995), An Interpretive Introduction to Quantum Field Theory. Princeton, NJ: Princeton University Press.Google Scholar
Wallace, David (2001), “The Emergence of Particles from Bosonic Quantum Field Theory”, http://xxx.lanl.gov/quant-ph/0112149.Google Scholar
Wallace, David (2006), “In Defence of Naiveté: The Conceptual Status of Lagrangian Quantum Field Theory”, In Defence of Naiveté: The Conceptual Status of Lagrangian Quantum Field Theory 151:3380.Google Scholar
Wess, Julius, and Bagger, Jonathan (1992), Supersymmetry and Supergravity. 2nd ed. Princeton, NJ: Princeton University Press.Google Scholar
Wightman, Arthur S. (1959), “Quelques problèmes mathématiques de la théorie quantique relativiste”, in Les problèmes mathématiques de la théorie quantique des champs. New York: Centre National de la Recherche Scientifique, 138.Google Scholar
Wightman, Arthur S. (1963), “Recent Achievements of Axiomatic Field Theory”, in Theoretical Physics. Vienna: International Atomic Energy Agency, 1158.Google Scholar
Wightman, Arthur S. (1986), “Some Lessons of Renormalization Theory”, in Boer, J. de, Dal, E., and Ulfbeck, O. (eds.), The Lesson of Quantum Theory. New York: Elsevier, 201226.Google Scholar