Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. -/- This expanded edition features several additional chapters, as (...) well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. (shrink)

v. 1. Classical theory.--v. 2. Functional formulation of S-matrix theory.

This document is a set of notes I took on QFT as a graduate student at the University of Pennsylvania, mainly inspired in lectures by Burt Ovrut, but also working through Peskin and Schroeder (1995), as well as David Tong’s lecture notes available online. They take a slow pedagogical approach to introducing classical field theory, Noether’s theorem, the principles of quantum mechanics, scattering theory, and culminating in the derivation of Feynman diagrams.

Examining relativistic quantum field theory we claim that its description of subnuclear phenomena can be understood most adequately from a semiotic point of view. The paper starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theories. The particular methods, by which these different aspects have to be accessed, can be described as distinct facets of quantum field theory. They differ with respect to the relation between quantum fields and (...) associated particles, and, as we shall argue, should be interpreted as complementary (semiotic) codes. Viewing physical theories as symbolic constructions already came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably, as we will point out, with the work of Helmholtz, Hertz, Poincaré, and later on Weyl. Since the epistemological questions posed there are heightened with regard to quantum field theory, we considerably widen their approach and relate it to recent discussions in the philosophy of science, like structural realism and quasi-autonomous domains. (shrink)

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 and acknowledges the irreducible cognitive elements in its representation. The interpretation is based on an analysis of our ways of thinking as the are embedded in the logical structure of QFT. The author argues that philosophical categories are significant only if they play active and essential roles in our knowledge and hence constitute part of the theories in actual use. Thus she regards physical theories as primary, extracts their categorical structure, and uses it to rethink key philosophical questions. Among the questions this book tries to answer are: What are the quantum properties independent of measurements? How do we refer to individual things in a continuous field? How do theories relate to objects? What are the general conditions of the world and of our ways of thinking that make possible our knowledge of the microscopic realm, which is so intangible and counterintuitive? As a penetrating analysis of vital themes in contemporary science, the book will engage the interest of students and professionals in physics and philosophy alike. (shrink)

Axiomatic quantum field theory is one approach to the project of merging the special theory of relativity with that of ordinary quantum mechanics. The project begins with the postulation of a set of axioms. Axioms should be motivated by reasonable physical principles in a way that illustrates how a given axiom is true. Motivations are often grounded in the principles of the parent theories: ordinary quantum mechanics or the theory of special relativity. Amongst the set of axioms first (...) proposed by Haag and Kastler in 1963 is the axiom of microcausality. Microcausality requires the observables of regions at space-like separation to commute. This thesis seeks to answer the question ‘What principles from the special theory of relativity or ordinary quantum mechanics motivate, or justify, accepting microcausality as an axiom?’ The first chapter will provide the necessary background to investigate this question and the second chapter will undertake that investigation. In conclusion, microcausality cannot be well-motivated by individual principles rooted in the special theory of relativity or ordinary quantum mechanics. (shrink)

The field theory of free strings is analyzed in gauges in which the two-dimensional metric along the string worldsheet remains as a dynamical variable. Hamiltonian-based BRST methods are used. The cohomology of the complete BRST charge is computed. Equivalence with the usual approach is explicitly established.

Neuroscience investigates how neuronal processing circuits work, but it has problems explaining experiences this way. For example, it hasn’t explained how colour and shape circuits bind together in visual processing, nor why colours and other qualia are experienced so differently yet processed by circuits so similarly, nor how to get from processing circuits to pictorial images spread across inner space. Some theorists turn from these circuits to their electromagnetic fields to deal with such difficulties concerning the mind’s qualia, unity, privacy, (...) and causality. They include Kohler, Libet, Popper, Lindahl, Arhem, Charman, Pockett, John, McFadden, Fingelkurts, Maxwell, and Jones. They’re classifiable as computationalist, reductionist, dualist, realist, interactionist, epiphenomenalist, globalist, and localist. However, they’ve never been analysed together as a whole, which hinders evaluations of them. This article tries to rectify this. It concludes that while field theories face challenges, they aren’t easily dismissed, for they draw on considerable evidence and may avoid serious problems in neuroscience concerning the mind’s qualia, unity, causality, and ontology. (shrink)

Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. In a rather informal sense QFT is the extension of quantum mechanics (QM), dealing with particles, over to fields, i.e. systems with an infinite number of degrees of freedom. (See the entry on quantum mechanics.) In the last few years QFT has become a more widely discussed topic in philosophy of science, with questions ranging from methodology and semantics to ontology. QFT taken seriously in (...) its metaphysical implications seems to give a picture of the world which is at variance with central classical conceptions of particles and fields, and even with some features of QM. -/- The following sketches how QFT describes fundamental physics and what the status of QFT is among other theories of physics. Since there is a strong emphasis on those aspects of the theory that are particularly important for interpretive inquiries, it does not replace an introduction to QFT as such. One main group of target readers are philosophers who want to get a first impression of some issues that may be of interest for their own work, another target group are physicists who are interested in a philosophical view upon QFT. (shrink)

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. *Received June 2009; revised August 2009. †To contact the author, please write to: Department of Philosophy, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada; e‐mail: dlfraser@uwaterloo.ca. (shrink)

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.

Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effective field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a (...) given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispensable. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation. (shrink)

A bivertical classical field theory includes the Newtonian mechanics and Maxwell's electromagnetic field theory as the special cases. This unification allows one to recognize the formal analogies among Newtonian mechanics and Maxwell's electrodynamics.

Effective Field Theory (EFT) is the successful paradigm underlying modern theoretical physics, including the "Core Theory" of the Standard Model of particle physics plus Einstein's general relativity. I will argue that EFT grants us a unique insight: each EFT model comes with a built-in specification of its domain of applicability. Hence, once a model is tested within some domain (of energies and interaction strengths), we can be confident that it will continue to be accurate within that domain. Currently, the (...) Core Theory has been tested in regimes that include all of the energy scales relevant to the physics of everyday life (biology, chemistry, technology, etc.). Therefore, we have reason to be confident that the laws of physics underlying the phenomena of everyday life are completely known. (shrink)

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical (...) class='Hi'>field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras. (shrink)

Recently doubts have been raised about the ability of pilot wave theories with field ontology to recover the predictions of quantum field theory. In particular, Struyve has questioned that the overlap between wave functionals of macroscopically different states with fixed particle number is really non-significant.With numerical computations and some further plausibility arguments we show that the overlap between n-particle states in field theory decreases almost exponentially with the number of particles and becomes non-significant already for small (...) particle numbers. (shrink)

A theory is presented in which a field depends not only on spacetime coordinates xμ, but also on a Lorentz-invariant parameter τ. Such a theory is conceptually and technically simple and manifestly covariant at every step. The generator of evolution and the generator of spacetime translations and Lorentz transformations are obtained in a straightforward way. In the quantized theory the Heisenberg equation of motion is written in a covariant form and is equivalent to the field equation. The equal (...) τ commutator between the field and its canonically conjugate momentum is just proportional to the spacetime δ function. Finally comparison with the conventional field theory is done, and it is found that the expectation value of the momentum operator in the on shell states is the same. (shrink)

Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of “gauge” transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.

The hard problem of consciousness arises in most incarnations of present day physicalism. Why should certain physical processes necessarily be accompanied by experience? One possible response is that physicalism itself should be modified in order to accommodate experience: But, modified how? In the present work, we investigate whether an ontology derived from quantum field theory can help resolve the hard problem. We begin with the assumption that experience cannot exist without being accompanied by a subject of experience (SoE). While (...) people well versed in Indian philosophy will not find that statement problematic, it is still controversial in the analytic tradition. Luckily for us, Strawson has elaborately defended the notion of a thin subject—an SoE which exhibits a phenomenal unity with different types of content (sensations, thoughts etc.) occurring during its temporal existence. Next, following Stoljar, we invoke our ignorance of the true physical as the reason for the explanatory gap between present day physical processes (events, properties) and experience. We are therefore permitted to conceive of thin subjects as related to the physical via a new, yet to be elaborated relation. While this is difficult to conceive under most varieties of classical physics, we argue that this may not be the case under certain quantum field theory ontologies. We suggest that the relation binding an SoE to the physical is akin to the relation between a particle and (quantum) field. In quantum field theory, a particle is conceived as a coherent excitation of a field. Under the right set of circumstances, a particle coalesces out of a field and dissipates. We suggest that an SoE can be conceived as akin to a particle—a SelfOn—which coalesces out of physical fields, persists for a brief period of time and then dissipates in a manner similar to the phenomenology of a thin subject. Experiences are physical properties of selfons with the constraint (specified by a similarity metric) that selfons belonging to the same natural kind will have similar experiences. While it is odd at first glance to conceive of subjects of experience as akin to particles, the spatial and temporal unity exhibited by particles as opposed to fields and the expectation that selfons are new kinds of particles, paves the way for cementing this notion. Next, we detail the various no-go theorems in most versions of quantum field theory and discuss their impact on the existence of selfons. Finally, we argue that the time is ripe for a rejuvenated Indian philosophy to begin tackling the three-way relationship between SoEs (which may become equivalent to jivas in certain Indian frameworks), phenomenal content and the physical world. With analytic philosophy still struggling to come to terms with the complex worlds of quantum field theory and with the relative inexperience of the western world in arguing the jiva-world relation, there is a clear and present opportunity for Indian philosophy to make a worldcentric contribution to the hard problem of experience. (shrink)

The field theoretic approach of the target article is simplified by setting the parameters of the dynamical field equation so that the system is near the critical point between cooperative and non-cooperative dynamics. However, embodiment of cognitive development would require a closer connection between the dynamical field interactions and the physiology of the cerebral cortex.

The metaphysical commitments of quantum field theory are examined. A thesis of underdetermination as between field and particle approaches to the "elementary particles" is argued for but only if a disputed notion of transcendental individuality is admitted. The superiority of the field approach is further emphasized in the context of heuristics.

In light of Hawking radiation’s empirical undetectability, physicists have attempted to establish it as universal—as a phenomenon that should appear regardless of the possible details of quantum gravity, whatever those details might be. But, as pointed out in a recent article by Gryb, Palacios, and Thébault, these universality arguments for Hawking radiation seem broadly unconvincing compared to the Wilsonian renormalization-group universality arguments for condensed matter physics. Motivated by their apparent failure, compared with the overwhelming success of universality arguments in so (...) many other contexts, I address the question: in which situations should we expect to be able to construct successful universality arguments? In other words, which situations are ‘universality-argument-apt’? I distinguish between two notions of success for a universality argument: ‘strength’ and ‘relevance’. I argue that we should only expect to be able to construct universality arguments that are successful in the sense of being significantly relevant to a given domain if we know enough about how that domain’s micro-physics is structured, we are able to empirically test the domain’s macro-behaviour, or if we are in both situations at once. These conditions are useful, most obviously, as a clarification of what universality arguments can do. But I argue that they are also useful for two less direct reasons: they clarify the status of analogue experimentation and thereby show us where we stand in our search for empirical confirmation of Hawking radiation. (shrink)

Coping with the Future: Theories and Practices of Divination in East Asia. Edited by Michael Lackner. Sinica Leidensia, vol. 138. Leiden: Brill, 2017. Pp. xvi + 586. €149, $172.

How do brains create all our different colors, pains, and other conscious qualities? These various qualia are the most essential aspects of consciousness. Yet standard neuroscience (primarily based on synaptic information processing) has not found the synaptic-firing codes, sometimes described as the “spike code,” to account for how these qualia arise and how they unite to form complex perceptions, emotions, et cetera. Nor is it clear how to get from these abstract codes to the qualia we experience. But electromagnetic (...) class='Hi'>field (versus synaptic) approaches to how qualia arise have been offered in recent years by Pockett, McFadden, Jones, Bond, Ward and Guevera, Keppler and Shani, Hunt and Schooler, et cetera. These EM-field approaches show promise in offering more viable accounts of qualia. Yet, until now, they have not been evaluated together. We review various EM field theories of qualia, highlight their strengths and weaknesses, and contrast these theories with standard neuroscience approaches. -/- . (shrink)

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 that informs this view is motivated by nonrelativistic intuitions associated with the structure of classical spacetimes, and hence should be abandoned. Second, the relations between RQFTs and NQFTs also suggest that routes to quantum gravity are more varied than is typically acknowledged. The second half of this essay is concerned with mapping out some of this conceptual space. (shrink)

This paper engages with Manuel DeLanda’s Deleuze-inspired ‘assemblage theory’ from a perspective sympathetic to Pierre Bourdieu’s field theory. It first outlines DeLanda’s proposed new ‘philosophy of society’, focusing on his major works in this vein, and registers some scepticism as to its originality for sociology. It then introduces and responds to DeLanda’s critique of Bourdieu. Rather than simply reject assemblage theory outright, however, I draw on selected insights from DeLanda to push field theory in new directions. More specifically, (...) I conceptualise the interplay of fields and assemblages and use notions of ‘exteriority’ and ‘possibility space’ to help conceive individual plurality of social positioning and its effects for subjectivity and practice. (shrink)

Galileo's Error (Goff, 2019) leaves important questions unasked and hence unanswered. I focus on two of these: the question of what a theory of consciousness is supposed to accomplish, and the question of what the materialismâ–“dualismâ–“panpsychism debate is actually about.

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.

This article summarizes a variety of current as well as previous research in support of a new theory of consciousness. Evidence has been steadily accumulating that information about a stimulus complex is distributed to many neuronal populations dispersed throughout the brain and is represented by the departure from randomness of the temporal pattern of neural discharges within these large ensembles. Zero phase lag synchronization occurs between discharges of neurons in different brain regions and is enhanced by presentation of stimuli. This (...) evidence further suggests that spatiotemporal patterns of coherence, which have been identified by spatial principal component analysis, may encode a multidimensional representation of a present or past event. How such distributed information is integrated into a holistic percept constitutes the binding problem. How a percept defined by a spatial distribution of nonrandomness can be subjectively experienced constitutes the problem of consciousness. Explanations based on a discrete connectionistic network cannot be reconciled with the relevant facts. Evidence is presented herein of invariant features of brain electrical activity found to change reversibly with loss and return of consciousness in a study of 176 patients anesthetized during surgical procedures. A review of relevant research areas, as well as the anesthesia data, leads to a postulation that consciousness is a property of quantumlike processes, within a brain field resonating within a core of structures, which may be the neural substrate of consciousness. This core includes regions of the prefrontal cortex, the frontal cortex, the pre- and paracentral cortex, thalamus, limbic system, and basal ganglia. (shrink)

With the present paper I maintain that the group field theory (GFT) approach to quantum gravity can help us clarify and distinguish the problems of spacetime emergence from the questions about the nature of the quanta of space. I will show that the mechanism of phase transition suggests a form of indifference between scales (or phases) and that such an indifference allows us to black-box questions about the nature of the ontology of the fundamental levels of the theory. I (...) consider the GFT approach to quantum gravity which derives spacetime as an emergent property from abstract non-geometrical tetrahedra through a processes of phase transition. Because the physical interpretation of the tetrahedra is problematic in view of their (non)-spatiotemporal nature, I will apply the considerations about phase transitions to GFT and conclude that the fundamental ontology of the theory and the mechanism of spacetime emergence can and should be treated separately. (shrink)

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. (...) In this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

Unitary field theories and “SUPER-GUT” theories work with an universal continuum, the structured spacetime of R. Descartes, B. Spinoza, B. Riemann, and A. Einstein, or a (Machian (1–3) ) structured vacuum according the quantum theory of unitary fields (Dirac, (4,5) and Heisenberg (6–8) ). The atomistic aspect of the substantial world is represented by the fundamental constants which are invariant against “all transformations” and which “depend on nothings” (Planck (9–11) ). A satisfactory unitary theory has to involve (...) these constants like the mathematical numbers. Today, Planck's conception of the three elementary constants ħ, c, and G may be the key to general relativistic quantum field theory like unitary theory. However, the elementary constants are a question of measurement-theory, also.According to Popper's theory (12–16) of induction, such unitary theories are “universal explaining theories.” The fundamental constants involve the complementarity between the universal statements in unitary theory and the “basic statements” in the language of classical observables. (shrink)

A correspondence theory of truth explains truth in terms of various correspondence relations (e.G., Reference) between words and the extralinguistic world. What are the consequences of quine's doctrine of indeterminacy for correspondence theories? in "ontological relativity" quine implicitly claims that correspondence theories are impossible; that is what the doctrine of 'relative reference' amounts to. But quine's doctrine of relative reference is incoherent. Those who think the indeterminacy thesis valid should not try to relativize reference, They should abandon the (...) relation and replace it by certain more general correspondence relations between words and extralinguistic objects. Doing so will not interfere with the task of defining truth in terms of correspondence relations. (shrink)

After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles, the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical (...) notions. Being discrete it can describe localized states and measurements, solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (shrink)

Field theory is often criticized because sociologists applying it fail to follow two seminal rules: the three key concepts of field theory—capital, habitus, and field structure—must be implemented in relation to each other and reconstructed for the historically specific moment of their application. I claim that Bourdieu developed his conceptual tools in response to Bachelard’s insight that scientific progress requires a break from common sense. Once we appreciate the epistemological foundation of field theory concepts, we can (...) better appreciate the rules for their application, avoid their typical criticism, and further improve them. (shrink)

The mean-field theory with the use of the slave-boson functional method has been generalized to take account of the spin- and/or orbital-ordered state in the doubly degenerate Hubbard model. Numerical calculations are presented of the antiferromagnetic orbital-ordered state in the half-filled simple-cubic model. The orbital order in the present theory is much reduced compared with that in the Hartree–Fock approximation because of the large orbital fluctuations. From a comparison of the ground-state energy, the antiferromagnetic orbital state is shown to (...) be unstable against the antiferromagnetic spin state, although the situation becomes reversed when the exchange interaction is negative. (shrink)

In this paper I elicit a prediction from structural realism and compare it, not to a historical case, but to a contemporary scientific theory. If structural realism is correct, then we should expect physics to develop theories that fail to provide an ontology of the sort sought by traditional realists. If structure alone is responsible for instrumental success, we should expect surplus ontology to be eliminated. Quantum field theory (QFT) provides the framework for some of the best confirmed (...) theories in science, but debates over its ontology are vexed. Rather than taking a stand on these matters, the structural realist can embrace QFT as an example of just the kind of theory SR should lead us to expect. Yet, it is not clear that QFT meets the structuralist's positive expectation by providing a structure for the world. In particular, the problem of unitarily inequivalent representations threatens to undermine the possibility of QFT providing a unique structure for the world. In response to this problem, I suggest that the structuralist should endorse pluralism about structure. (shrink)