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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. D. Anselmi (2003). A New Perspective on the Philosophical Implications of Quantum Field Theory. 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.
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  2. A. Arageorgis, J. Earman & L. Ruetsche (2002). Weyling the Time Away: The Non-Unitary Implementability of Quantum Field Dynamics on Curved Spacetime. 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.
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  3. Aristidis Arageorgis (1995). Fields, Particles, and Curvature: Foundations and Philosophical Aspects of Quantum Field Theory in Curved Spacetime. 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 (...)
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  4. Aristidis Arageorgis, John Earman & and Laura Ruetsche (2003). Fulling Non‐Uniqueness and the Unruh Effect. 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 (...)
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  5. Sunny Y. Auyang (2000). Mathematics and Reality: Two Notions of Spacetime in the Analytic and Constructionist Views of Gauge Field Theories. 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.
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  6. Sunny Y. Auyang (1995). How is Quantum Field Theory Possible? 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 (...)
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  7. Jonathan Bain (2013). Effective Field Theories. In Robert Batterman (ed.), The Oxford Handbook of Philosophy of Physics. OUP Usa 224.
  8. Jonathan Bain (2013). Emergence in Effective Field Theories. 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.
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  9. Jonathan Bain (2013). CPT Invariance, the Spin-Statistics Connection, and the Ontology of Relativistic Quantum Field Theories. 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 (...)
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  10. Jonathan Bain (2011). Quantum Field Theories in Classical Spacetimes and Particles. 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 (...)
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  11. Jonathan Bain (2010). Relativity and Quantum Field Theory. 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 (...)
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  12. Jonathan Bain (2005). Quantum Processes: A Whiteheadian Interpretation of Quantum Field Theory. Studies in History and Philosophy of Science Part B 36 (4):680-690.
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  13. Jonathan Bain (2000). Against Particle/Field Duality: Asymptotic Particle States and Interpolating Fields in Interacting Qft (Or: Who's Afraid of Haag's Theorem?). [REVIEW] 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 (...)
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  14. Jonathan Bain (1998). Weinberg on QFT: Demonstrative Induction and Underdetermination. 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.
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  15. David Baker (2009). Against Field Interpretations of Quantum Field Theory. 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 (...)
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  16. David John Baker (2013). Identity, Superselection Theory, and the Statistical Properties of Quantum Fields. 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 (...)
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  17. David John Baker & Hans Halvorson (2013). How is Spontaneous Symmetry Breaking Possible? Understanding Wigner's Theorem in Light of Unitary Inequivalence. 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 (...)
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  18. David Baker & Hans Halvorson (2010). Antimatter. 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 (...)
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  19. Andreas Bartels (1999). Objects or Events?: Towards an Ontology for Quantum Field Theory. 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 (...)
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  20. A. F. Bennett (2015). Spin-Statistics Connection for Relativistic Quantum Mechanics. 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.
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  21. D. Bohm & B. J. Hiley (1991). On the Relativistic Invariance of a Quantum Theory Based on Beables. 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.
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  22. Nazim Bouatta & Jeremy Butterfield (2015). On Emergence in Gauge Theories at the ’T Hooft Limit‘. 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: (...)
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  23. Harvey R. Brown & Rom Harré (eds.) (1988). Philosophical Foundations of Quantum Field Theory. 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.
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  24. Paul Busch & Franklin E. Schroeck Jr (1989). On the Reality of Spin and Helicity. Foundations of Physics 19 (7):807-872.
  25. Jeremy Butterfield (1993). The Philosophy of Vacuum. Philosophical Books 34 (4):253-256.
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  26. Tian Yu Cao (2003). Appendix: Ontological Relativity and Fundamentality – is QFT the Fundamental Theory? Synthese 136 (1):25 - 30.
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  27. Tian Yu Cao (2003). Structural Realism and the Interpretation of Quantum Field Theory. Synthese 136 (1):3 - 24.
  28. Tian Yu Cao & Silvan S. Schweber (1993). The Conceptual Foundations and the Philosophical Aspects of Renormalization Theory. Synthese 97 (1):33 - 108.
  29. C. Carson (1996). The Peculiar Notion of Exchange Forces--I: Origins in Quantum Mechanics, 1926-1928. Studies in History and Philosophy of Science Part B 27 (1):23-45.
  30. Elena Castellani (2002). Reductionism, Emergence, and Effective Field Theories. 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.
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  31. Jordi Cat (2000). Must the Microcausality Condition Be Interpreted Causally?: Beyond Reduction and Matters of Fact. 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 (...)
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  32. Jordi Cat (2000). Must the Microcausality Condition Be Interpreted Causally? 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 (...)
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  33. Rob Clifton (1996). Perspectives on Quantum Reality Non-Relativistic, Relativistic, and Field-Theoretic.
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  34. Rob Clifton & Hans Halvorson (2001). Are Rindler Quanta Real? Inequivalent Particle Concepts in Quantum Field Theory. 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 (...)
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  35. Rob Clifton & Hans Halvorson (2001). Entanglement and Open Systems in Algebraic Quantum Field Theory. 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 (...)
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  36. Rob Clifton & Laura Ruetsche (1999). Changing the Subject: Redei on Causal Dependence and Screening Off in Relativistic Quantum Field Theory. 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.
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  37. Rob Clifton & Laura Ruetsche (1999). 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. Philosophy of Science 66 (3).
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  38. Fabrizio Coppola (2013). The Philosophical Basis of the Arrangement Field Theory. Scientia 124.
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  39. Michael Danos (1997). Ward-Takahashi Identities and Noether's Theorem in Quantum Field Theory. 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.
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  40. B. DeFacio (1975). Causal Independence in Algebraic Quantum Field Theory. 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 (...)
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  41. Dennis Dieks, Events and Covariance in the Interpretation of Quantum Field Theory.
    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 (...)
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  42. Sergio Doplicher (2010). Spin and Statistics and First Principles. 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 (...)
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  43. Jan Dubnicka (2009). Philosophical and Methodological Problems in Building the Theory of Quantum Gravitation. 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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  44. Maxim Dvornikov (2012). Canonical Quantization of a Massive Weyl Field. Foundations of Physics 42 (11):1469-1479.
    We construct a consistent theory of a quantum massive Weyl field. We start with the formulation of the classical field theory approach for the description of massive Weyl fields. It is demonstrated that the standard Lagrange formalism cannot be applied for the studies of massive first-quantized Weyl spinors. Nevertheless we show that the classical field theory description of massive Weyl fields can be implemented in frames of the Hamilton formalism or using the extended Lagrange formalism. Then we carry out a (...)
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  45. John Earman (2014). No Superluminal Propagation for Classical Relativistic and Relativistic Quantum Fields. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 48:102-108.
    A criterion is proposed to ensure that classical relativistic fields do not propagate superluminally. If this criterion does indeed serve as a sufficient condition for no superluminal propagation it follows that various other criteria found in the physics literature cannot serve as necessary conditions since they can fail although the proffered condition holds. The rejected criteria rely on energy conditions that are believed to hold for most classical fields used in actual applications. But these energy conditions are known to fail (...)
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  46. John Earman & Doreen Fraser (2006). Haag's Theorem and its Implications for the Foundations of Quantum Field Theory. Erkenntnis 64 (3):305 - 344.
    Although the philosophical literature on the foundations of quantum field theory recognizes the importance of Haag’s theorem, it does not provide a clear discussion of the meaning of this theorem. The goal of this paper is to make up for this deficit. In particular, it aims to set out the implications of Haag’s theorem for scattering theory, the interaction picture, the use of non-Fock representations in describing interacting fields, and the choice among the plethora of the unitarily inequivalent representations of (...)
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  47. John Earman & Giovanni Valente (2014). Relativistic Causality in Algebraic Quantum Field Theory. International Studies in the Philosophy of Science 28 (1):1-48.
    This paper surveys the issue of relativistic causality within the framework of algebraic quantum field theory . In doing so, we distinguish various notions of causality formulated in the literature and study their relationships, and thereby we offer what we hope to be a useful taxonomy. We propose that the most direct expression of relativistic causality in AQFT is captured not by the spectrum condition but rather by the axiom of local primitive causality, in that it entails a form of (...)
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  48. James D. Edmonds Jr (1974). Complex Energies in Relativistic Quantum Theory. Foundations of Physics 4 (4):473-479.
    A new four-component spin-1/2 wave equation for ordinary mass is discussed. It is shown that this equation has a conserved current not easily identified with a transition probability, only pure imaginary energy states, and is covariant. A tachyon-like Klein-Gordon equation is satisfied by this equation, but rest states are explicitly constructed.
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  49. Matthias Egg (2014). 9 Particle Physics Without Particles? On Causal Realism in Quantum Field Theory. In Scientific Realism in Particle Physics: A Causal Approach. De Gruyter 149-174.
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  50. Albert Einstein (1960). Field Theories, Old and New. New York, Readex Microprint Corp..
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