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Summary Quantum field theory (QFT) is the framework of elementary particle physics; it is, in a nutshell, a mathematical framework in which one does quantum mechanics on fields. The metaphysical implications of quantum field theory are of particular interest to philosophers, and in the current literature there are two mainstream opposing views regarding the correct ontology of quantum field theory. According to one, the correct ontology of quantum field theory consists of point particles only, they are real, and fundamental, and fields are not. The other view claims that particles cannot exist, only fields. Also of interest to philosophers are the issues posed by effective field theories and renormalization theory; some philosophers reject conventional quantum field theory and argue for a new axiomatization of quantum field theory. 
Key works In the "fields-only" interpretation of QFT camp are Malament 1996, Fraser 2008, and Hobson 2012; Baker 2009 argues that neither the fields-only or particles-only ontologies are tenable. Wallace 2011 contains a summary and critique of the debate over whether we should adopt conventional or axiomatic quantum field theories in response to the issues posed by renormalization theory and effective field theories. 
Introductions The Stanford Encyclopedia article on Quantum Field Theory is an excellent introduction to the philosophical issues.  Zee's Quantum Field Theory in a Nutshell is a lucid introduction to the physics and mathematics of quantum field theory, and Peskin and Schroeder's Introduction to Quantum Field Theory is the canonical QFT textbook used by physicists. 
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  1. A New Perspective on the Philosophical Implications of Quantum Field Theory.D. Anselmi - 2003 - Synthese 135 (3):299 - 328.
    I discuss issues concerning the philosophical foundations andimplications of quantum field theory, renormalization inparticular. A new understanding of the correspondence principle,an unexpected role of perturbation theory and, most of all, acriterion to reduce the set of consistent theories frominfinitely many to finitely many, are the key concepts of atheoretical set-up that appears to overcome in a natural wayvarious consistency problems of quantum mechanics and offerseveral hints for further developments.
  2. Weyling the Time Away: The Non-Unitary Implementability of Quantum Field Dynamics on Curved Spacetime.A. Arageorgis, J. Earman & L. Ruetsche - 2002 - Studies in History and Philosophy of Science Part B 33 (2):151-184.
    The simplest case of quantum field theory on curved spacetime-that of the Klein-Gordon field on a globally hyperbolic spacetime-reveals a dilemma: In generic circumstances, either there is no dynamics for this quantum field, or else there is a dynamics that is not unitarily implementable. We do not try to resolve the dilemma here, but endeavour to spell out the consequences of seizing one or the other horn of the dilemma.
  3. Fields, Particles, and Curvature: Foundations and Philosophical Aspects of Quantum Field Theory in Curved Spacetime.Aristidis Arageorgis - 1995 - Dissertation, University of Pittsburgh
    The physical, mathematical, and philosophical foundations of the quantum theory of free Bose fields in fixed general relativistic spacetimes are examined. It is argued that the theory is logically and mathematically consistent whereas semiclassical prescriptions for incorporating the back-reaction of the quantum field on the geometry lead to inconsistencies. Still, the relations and heuristic value of the semiclassical approach to canonical and covariant schemes of quantum gravity-plus-matter are assessed. Both conventional and rigorous formulations of the theory and of its principal (...)
  4. Fulling Non‐Uniqueness and the Unruh Effect.Aristidis Arageorgis, John Earman & and Laura Ruetsche - 2003 - Philosophy of Science 70 (1):164-202.
    We discuss the intertwined topics of Fulling non-uniqueness and the Unruh effect. The Fulling quantization, which is in some sense the natural one for an observer uniformly accelerated through Minkowski spacetime to adopt, is often heralded as a quantization of the Klein-Gordon field which is both physically relevant and unitarily inequivalent to the standard Minkowski quantization. We argue that the Fulling and Minkowski quantizations do not constitute a satisfactory example of physically relevant, unitarily inequivalent quantizations, and indicate what it would (...)
  5. Mathematics and Reality: Two Notions of Spacetime in the Analytic and Constructionist Views of Gauge Field Theories.Sunny Y. Auyang - 2000 - Philosophy of Science 67 (3):494.
    This paper presents two interpretations of the fiber bundle formalism that is applicable to all gauge field theories. The constructionist interpretation yields a substantival spacetime. The analytic interpretation yields a structural spacetime, a third option besides the familiar substantivalism and relationalism. That the same mathematical formalism can be derived in two different ways leading to two different ontological interpretations reveals the inadequacy of pure formal arguments.
  6. How is Quantum Field Theory Possible?Sunny Y. Auyang - 1995 - Oxford University Press.
    Quantum field theory (QFT) combines quantum mechanics with Einstein's special theory of relativity and underlies elementary particle physics. This book presents a philosophical analysis of QFT. It is the first treatise in which the philosophies of space-time, quantum phenomena, and particle interactions are encompassed in a unified framework. Describing the physics in nontechnical terms, and schematically illustrating complex ideas, the book also serves as an introduction to fundamental physical theories. The philosophical interpretation both upholds the reality of the quantum world (...)
  7. Interpreting Effective Field Theories.Jonathan Bain - manuscript -
    An effective field theory is a theory of the dynamics of a physical system at energies small compared to a given cut-off. Low-energy states with respect to this cut-off are effectively independent of states at high energies; hence one may study the low-energy dynamics without the need for a detailed description of the high-energy dynamics. Many authors have suggested that, because of the essential role the cut-off plays in the standard method of constructing an EFT, an appropriate interpretation of an (...)
  8. Effective Field Theories.Jonathan Bain - 2013 - In Robert Batterman (ed.), The Oxford Handbook of Philosophy of Physics. Oup Usa. pp. 224.
  9. Emergence in Effective Field Theories.Jonathan Bain - 2013 - European Journal for Philosophy of Science 3 (3):257-273.
    This essay considers the extent to which a concept of emergence can be associated with Effective Field Theories (EFTs). I suggest that such a concept can be characterized by microphysicalism and novelty underwritten by the elimination of degrees of freedom from a high-energy theory, and argue that this makes emergence in EFTs distinct from other concepts of emergence in physics that have appeared in the recent philosophical literature.
  10. Pragmatists and Purists on CPT Invariance in Relativistic Quantum Field Theories.Jonathan Bain - unknown -
    Philosophers of physics are split on whether foundational issues in relativistic quantum field theory should be framed within pragmatist approaches, which trade mathematical rigor for the ability to formulate non-trivial interacting models, or purist approaches, which trade the ability to formulate non-trivial interacting models for mathematical rigor. This essay addresses this debate by viewing it through the lens of the CPT theorem. I first consider two formulations of the CPT theorem, one purist and the other pragmatist, and extract from them (...)
  11. CPT Invariance, the Spin-Statistics Connection, and the Ontology of Relativistic Quantum Field Theories.Jonathan Bain - 2013 - Erkenntnis 78 (4):797-821.
    CPT invariance and the spin-statistics connection are typically taken to be essential properties in relativistic quantum field theories (RQFTs), insofar as the CPT and Spin-Statistics theorems entail that any state of a physical system characterized by an RQFT must possess these properties. Moreover, in the physics literature, they are typically taken to be properties of particles. But there is a Received View among philosophers that RQFTs cannot fundamentally be about particles. This essay considers what proofs of the CPT and Spin-Statistics (...)
  12. Quantum Field Theories in Classical Spacetimes and Particles.Jonathan Bain - 2011 - Studies in History and Philosophy of Science Part B 42 (2):98-106.
    According to a Received View, relativistic quantum field theories (RQFTs) do not admit particle interpretations. This view requires that particles be localizable and countable, and that these characteristics be given mathematical expression in the forms of local and unique total number operators. Various results (the Reeh-Schlieder theorem, the Unruh Effect, Haag's theorem) then indicate that formulations of RQFTs do not support such operators. These results, however, do not hold for nonrelativistic QFTs. I argue that this is due to the absolute (...)
  13. Quantum Field Theories in Classical Spacetimes and Particles.Jonathan Bain - 2011 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42 (2):98-106.
  14. Relativity and Quantum Field Theory.Jonathan Bain - 2010 - In V. Petkov (ed.), Space, Time and Spacetime.
    Relativistic quantum field theories (RQFTs) are invariant under the action of the Poincaré group, the symmetry group of Minkowski spacetime. Non-relativistic quantum field theories (NQFTs) are invariant under the action of the symmetry group of a classical spacetime; i.e., a spacetime that minimally admits absolute spatial and temporal metrics. This essay is concerned with cashing out two implications of this basic difference. First, under a Received View, RQFTs do not admit particle interpretations. I will argue that the concept of particle (...)
  15. Quantum Processes: A Whiteheadian Interpretation of Quantum Field Theory.Jonathan Bain - 2005 - Studies in History and Philosophy of Science Part B 36 (4):680-690.
  16. Quantum Processes: A Whiteheadian Interpretation of Quantum Field Theory.Jonathan Bain - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (4):680-690.
  17. Against Particle/Field Duality: Asymptotic Particle States and Interpolating Fields in Interacting Qft (Or: Who's Afraid of Haag's Theorem?). [REVIEW]Jonathan Bain - 2000 - Erkenntnis 53 (3):375-406.
    This essay touches on a number of topics in philosophy of quantum field theory from the point of view of the LSZ asymptotic approach to scattering theory. First, particle/field duality is seen to be a property of free field theory and not of interacting QFT. Second, it is demonstrated how LSZ side-steps the implications of Haag's theorem. Finally, a recent argument due to Redhead, Malament and Arageorgis against the concept of localized particle states is addressed. Briefly, the argument observes that (...)
  18. Weinberg on QFT: Demonstrative Induction and Underdetermination.Jonathan Bain - 1998 - Synthese 117 (1):1-30.
    In this essay I examine a recent argument by Steven Weinberg that seeks to establish local quantum field theory as the only type of quantum theory in accord with the relevent evidence and satisfying two basic physical principles. I reconstruct the argument as a demonstrative induction and indicate it's role as a foil to the underdetermination argument in the debate over scientific realism.
  19. Against Field Interpretations of Quantum Field Theory.David Baker - 2009 - British Journal for the Philosophy of Science 60 (3):585-609.
    I examine some problems standing in the way of a successful `field interpretation' of quantum field theory. The most popular extant proposal depends on the Hilbert space of `wavefunctionals.' But since wavefunctional space is unitarily equivalent to many-particle Fock space, two of the most powerful arguments against particle interpretations also undermine this form of field interpretation. IntroductionField Interpretations and Field OperatorsThe Wavefunctional InterpretationFields and Inequivalent Representations 4.1. The Rindler representation 4.2. Spontaneous symmetry breaking 4.3. Coherent representations The Fate of Fields (...)
  20. The Philosophy of Quantum Field Theory.David John Baker - unknown -
    If we divide our physical theories into theories of matter and theories of spacetime, quantum field theory is our most fundamental empirically successful theory of matter. As such, it has attracted increasing attention from philosophers over the past two decades, beginning to eclipse its predecessor theory of quantum mechanics in the philosophical literature. Here I survey some central philosophical puzzles about the theory's foundations.
  21. Identity, Superselection Theory, and the Statistical Properties of Quantum Fields.David John Baker - 2013 - Philosophy of Science 80 (2):262-285.
    The permutation symmetry of quantum mechanics is widely thought to imply a sort of metaphysical underdetermination about the identity of particles. Despite claims to the contrary, this implication does not hold in the more fundamental quantum field theory, where an ontology of particles is not generally available. Although permutations are often defined as acting on particles, a more general account of permutation symmetry can be formulated using superselection theory. As a result, permutation symmetry applies even in field theories with no (...)
  22. How is Spontaneous Symmetry Breaking Possible? Understanding Wigner's Theorem in Light of Unitary Inequivalence.David John Baker & Hans Halvorson - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4):464-469.
    We pose and resolve a puzzle about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator in a ground state's GNS representation. But Wigner's theorem guarantees that any symmetry's action on states is given by a unitary operator. How can this unitary operator fail to implement the symmetry in the GNS representation? We show how it is possible for a unitary operator of this (...)
  23. Antimatter.David Baker & Hans Halvorson - 2010 - British Journal for the Philosophy of Science 61 (1):93-121.
    Next SectionThe nature of antimatter is examined in the context of algebraic quantum field theory. It is shown that the notion of antimatter is more general than that of antiparticles. Properly speaking, then, antimatter is not matter made up of antiparticles—rather, antiparticles are particles made up of antimatter. We go on to discuss whether the notion of antimatter is itself completely general in quantum field theory. Does the matter–antimatter distinction apply to all field theoretic systems? The answer depends on which (...)
  24. Objects or Events?: Towards an Ontology for Quantum Field Theory.Andreas Bartels - 1999 - Philosophy of Science 66 (3):184.
    The recent work of Paul Teller and Sunny Auyang in the philosophy of Quantum Field Theory (QFT) has stimulated the search for the fundamental entities in this theory. In QFT, the classical notion of a particle collapses. The theory does not only exclude classical, i.e., spatiotemporally identifiable particles, but it makes particles of the same type conceptually indistinguishable. Teller and Auyang have proposed competing ersatz-ontologies to account for the 'loss of particles': field quanta vs. field events. Both ontologies, however, suffer (...)
  25. Spin-Statistics Connection for Relativistic Quantum Mechanics.A. F. Bennett - 2015 - Foundations of Physics 45 (4):370-381.
    The spin-statistics connection has been proved for nonrelativistic quantum mechanics . The proof is extended here to the relativistic regime using the parametrized Dirac equation. A causality condition is not required.
  26. On the Relativistic Invariance of a Quantum Theory Based on Beables.D. Bohm & B. J. Hiley - 1991 - Foundations of Physics 21 (2):243-250.
    We discuss the question of the relativistic invariance of a quantum theory based on beables, and we suggest the general outlines of one possible form of such a theory.
  27. On Emergence in Gauge Theories at the ’T Hooft Limit‘.Nazim Bouatta & Jeremy Butterfield - 2015 - European Journal for Philosophy of Science 5 (1):55-87.
    Quantum field theories are notoriously difficult to understand, physically as well as philosophically. The aim of this paper is to contribute to a better conceptual understanding of gauge quantum field theories, such as quantum chromodynamics, by discussing a famous physical limit, the ’t Hooft limit, in which the theory concerned often simplifies. The idea of the limit is that the number N of colours goes to infinity. The simplifications that can happen in this limit, and that we will consider, are: (...)
  28. Philosophical Foundations of Quantum Field Theory.Harvey R. Brown & Rom Harré (eds.) - 1988 - Oxford University Press.
    Quantum field theory, one of the most rapidly developing areas of contemporary physics, is full of problems of great theoretical and philosophical interest. This collection of essays is the first systematic exploration of the nature and implications of quantum field theory. The contributors discuss quantum field theory from a wide variety of standpoints, exploring in detail its mathematical structure and metaphysical and methodological implications.
  29. On the Reality of Spin and Helicity.Paul Busch & Franklin E. Schroeck Jr - 1989 - Foundations of Physics 19 (7):807-872.
  30. The Philosophy of Vacuum.Jeremy Butterfield - 1993 - Philosophical Books 34 (4):253-256.
  31. Renormalization for Philosophers.Jeremy Butterfield & Nazim Bouatta - unknown -
    We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites. Our motivation is that renormalization is undoubtedly one of the great ideas—and great successes--of twentieth-century physics. Also it has strongly influenced in diverse ways, how physicists conceive of physical theories. So it is of considerable philosophical interest. Second, we will briefly relate renormalization to Ernest Nagel's account of inter-theoretic relations, especially reduction. One theme will be a contrast between (...)
  32. Structural Realism and the Interpretation of Quantum Field Theory.Tian Yu Cao - 2003 - Synthese 136 (1):3 - 24.
  33. Appendix: Ontological Relativity and Fundamentality – is QFT the Fundamental Theory?Tian Yu Cao - 2003 - Synthese 136 (1):25 - 30.
  34. The Conceptual Foundations and the Philosophical Aspects of Renormalization Theory.Tian Yu Cao & Silvan S. Schweber - 1993 - Synthese 97 (1):33 - 108.
  35. The Peculiar Notion of Exchange Forces--I: Origins in Quantum Mechanics, 1926-1928.C. Carson - 1996 - Studies in History and Philosophy of Science Part B 27 (1):23-45.
  36. Reductionism, Emergence, and Effective Field Theories.Elena Castellani - 2002 - Studies in History and Philosophy of Science Part B 33 (2):251-267.
    In recent years, a ''change in attitude'' in particle physics has led to our understanding current quantum field theories as effective field theories (EFTs). The present paper is concerned with the significance of this EFT approach, especially from the viewpoint of the debate on reductionism in science. In particular, I shall show how EFTs provide a new and interesting case study in current philosophical discussion on reduction, emergence, and inter-level relationships in general.
  37. Must the Microcausality Condition Be Interpreted Causally?: Beyond Reduction and Matters of Fact.Jordi Cat - 2000 - Theoria 15 (1):59-85.
    The ’microcausality’ condition in quantum field theory is typically presented and justified on the basis of general principles of physical causality. I explore in detail a number of alternative causal interpretations of this condition. I conclude that none is fully satisfactory, independent of further and controversial assumptions about the object and scope of quantum field theories. In particular the stronger causalreadings require a fully reductionist and fundamentalist attitude to quantum field theory. I argue, in a deflationary spirit, for a reading (...)
  38. Must the Microcausality Condition Be Interpreted Causally?Jordi Cat - 2000 - Theoria 15 (1):59-85.
    The ’microcausality’ condition in quantum field theory is typically presented and justified on the basis of general principles of physical causality. I explore in detail a number of alternative causal interpretations of this condition. I conclude that none is fully satisfactory, independent of further and controversial assumptions about the object and scope of quantum field theories. In particular the stronger causalreadings require a fully reductionist and fundamentalist attitude to quantum field theory. I argue, in a deflationary spirit, for a reading (...)
  39. Perspectives on Quantum Reality Non-Relativistic, Relativistic, and Field-Theoretic.Rob Clifton - 1996 -
  40. Are Rindler Quanta Real? Inequivalent Particle Concepts in Quantum Field Theory.Rob Clifton & Hans Halvorson - 2001 - British Journal for the Philosophy of Science 52 (3):417-470.
    Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the "reality" of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e., inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a (...)
  41. Entanglement and Open Systems in Algebraic Quantum Field Theory.Rob Clifton & Hans Halvorson - 2001 - Studies in History and Philosophy of Science Part B 32 (1):1-31.
    Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum field theory (AQFT) provides a rigorous framework within which to analyse entanglement in the context of a fully relativistic formulation of quantum theory. What emerges from the analysis are new practical and theoretical limitations on an experimenter's ability to (...)
  42. Foundations of Statistical Physics, Spacetime Theories, and Quantum Field Theory-Changing the Subject: Redei on Causal Dependence and Screening Off in Relativistic Quantum Field Theory.Rob Clifton & Laura Ruetsche - 1999 - Philosophy of Science 66 (3).
  43. Changing the Subject: Redei on Causal Dependence and Screening Off in Relativistic Quantum Field Theory.Rob Clifton & Laura Ruetsche - 1999 - Philosophy of Science 66 (3):169.
    In a pair of articles (1996, 1997) and in his recent book (1998), Miklos Redei has taken enormous strides toward characterizing the conditions under which relativistic quantum field theory is a safe setting for the deployment of causal talk. Here, we challenge the adequacy of the accounts of causal dependence and screening off on which rests the relevance of Redei's theorems to the question of causal good behavior in the theory.
  44. The Philosophical Basis of the Arrangement Field Theory.Fabrizio Coppola - 2013 - Scientia 124.
  45. Ward-Takahashi Identities and Noether's Theorem in Quantum Field Theory.Michael Danos - 1997 - Foundations of Physics 27 (7):995-1009.
    The gap in the mathematical derivation of Noether’s theorem, and also of the Ward-Takahashi identities, caused by performing variation before quantization is closed by introduction of variational calculus for operator fields. It is demonstrated that both Noether’s theorem and the Ward-Takahashi identities retain full validity in quantum field theory.
  46. Causal Independence in Algebraic Quantum Field Theory.B. DeFacio - 1975 - Foundations of Physics 5 (2):229-237.
    Ekstein has shown that causal independence neither implies nor is implied by commutativity in an infinite-dimensional, reducible construction. DeFacio and Taylor have presented a finite-dimensional irreducible example of Ekstein's proposition. Avishai and Ekstein have shown that the original question regarding locality for algebraic quantum field theories remainsopen. We concur with that claim and offer additional arguments. A new denumerably infinite-dimensional, irreducible example is presented here which shows that a sort of “orthogonality” among operators is involved. Some observations on localC*-andW*-algebras are (...)
  47. Events and Covariance in the Interpretation of Quantum Field Theory.Dennis Dieks - unknown -
    In relativistic quantum field theory the notion of a local operation is regarded as basic: each open space-time region is associated with an algebra of observables representing possible measurements performed within this region. It is much more difficult to accommodate the notions of events taking place in such regions or of localized objects. But how can the notion of a local operation be basic in the theory if this same theory would not be able to represent localized measuring devices and (...)
  48. Spin and Statistics and First Principles.Sergio Doplicher - 2010 - Foundations of Physics 40 (7):719-732.
    It was shown in the early seventies that, in Local Quantum Theory (that is the most general formulation of Quantum Field Theory, if we leave out only the unknown scenario of Quantum Gravity) the notion of Statistics can be grounded solely on the local observable quantities (without assuming neither the commutation relations nor even the existence of unobservable charged field operators); one finds that only the well known (para)statistics of Bose/Fermi type are allowed by the key principle of local commutativity (...)
  49. Renormalized Quantum Field Theory and Cassirer's Epistemological System.H. G. Dosch - 1991 - Philosophia Naturalis 28 (part 1):97-114.
  50. Philosophical and Methodological Problems in Building the Theory of Quantum Gravitation.Jan Dubnicka - 2009 - Filozofia 64 (7):658-668.
    The paper deals with selected philosophical and methodological problems concerning the building of the quantum theory of gravitation, which is expected to unify general relativity and the quantum field theory into a single consistent and comprehensive theory. It outlines the basic ontological characteristics of such a theory, its structure and the limitations set upon it by the general relativity and the quantum field theory. Models of such a theory are described as well.
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