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)

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 (...) class='Hi'>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 translation of philosophical works is a topic that merits our attention both in respect of philosophical understanding and linguistic structure, although it is the former rather than the latter that prevails in discussions in Chinese academia. By drawing upon that branch of modern linguistics known as the lexical field theory, this paper attempts to analyze a host of related problems, including the following: readability as a basic requirement of translation, difficulties in translation caused by the syntactic-typological distance (...) of source and target languages, consistency of translated terms in general, consistency of semantically related terms in translation, consistency of translated terms regarding the syntagmatic axis and the paradigmatic axis, the use of monosyllabic, disyllabic, or polysyllabic Chinese terms in translation, translation of long or rare terms into Chinese, the middle way between ‘under-translation’ and ‘over-translation,’ identification of lexical fields for the systematic treatment of translated terms, and finally the in-depth understanding of original texts in their source languages as a prerequisite of any serious attempt of translation. (shrink)

Those enlightened philosophers of physics acknowledging some manner of descent from Kant’s ‘Copernican Revolution’ have long found encouragement and inspiration in the writings of Roberto Torretti. In this tribute, I focus on his “perspective on Kant’s perspective on objectivity” (2008), a short but highly stimulating attempt to extract the essential core of the Kantian doctrine that ‘objects of knowledge’ are constituted, not given, or with Roberto’s inimitable pungency, that “objectivity is an achievement, not a gift.” That essential core Roberto locates (...) in the Kantian notion of apperception, or self-activity, manifested in cognition in the idea of combination (Verbindung) or composition, which, Kant tells us, “among all ideas … is the one that is not given through objects, but can only be performed by the subject itself, because it is an act of self-activity” (B 130). I first rehearse Roberto’s proposal for how an imaginative interplay between sensibility and understanding can be fashioned via the productive imagination or power of reflective judgment (of the third Critique). In this way, the notion of composition in general, unfettered from needless period constraints issuing in “pure forms of sensibility” and “pure concepts of the understanding”, can be seen as the intellectual motor for the “free creation” of concepts celebrated by Einstein and others, furnishing structural scaffolding required to articulate and display physical objects and processes, a conceptual panoply that “cannot be fished out of the stream of impressions”. Roberto emphasizes that historical case studies are needed to evaluate his proposal, suggesting one himself, the continuous conceptual development inaugurated by Riemann’s Habilitätionsschrift (1854) resulting, some hundred years later, in the fiber bundle formalism of modern differential geometry and topology. I sketch a related suggestion, that the gauge groups of modern particle physics are the outcome of a similar line of conceptual advance, a structural scaffolding saving the phenomena of high-energy experiment within the framework of ‘effective field theory.’. (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)

Aron Gurwitsch’s Gestalt-inspired “field theory of consciousness” was introduced in the same period as Wolfgang Köhler’s theory of “electrical brain fields.” I consider parallels between these theories, drawing on results that have emerged in the last five years. First, I consider the claim that fields of consciousness supervene on electromagnetic fields in the brain, then I outline Gurwitsch’s field theory of consciousness, and finally I consider how the structures described by Gurwitsch might relate to structures (...) in the brain’s electro-magnetic field. Along the way, I expose a dogma (that qualia are paradigmatic conscious states) and develop an interpretation of Gurwitsch’s field theory. (shrink)

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: [email protected]. (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)

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.

Experiments in particle physics have hitherto failed to produce any significant evidence for the many explicit models of physics beyond the Standard Model (BSM) that had been proposed over the past decades. As a result, physicists have increasingly turned to model-independent strategies as tools in searching for a wide range of possible BSM effects. In this paper, we describe the Standard Model Effective Field Theory (SM-EFT) and analyse it in the context of the philosophical discussions about models, theories, (...) and (bottom-up) effective field theories. We find that while the SM-EFT is a quantum field theory, assisting experimentalists in searching for deviations from the SM, in its general form it lacks some of the characteristic features of models. Those features only come into play if put in by hand or prompted by empirical evidence for deviations. Employing different philosophical approaches to models, we argue that the case study suggests not to take a view on models that is overly permissive because it blurs the lines between the different stages of the SM-EFT research strategies and glosses over particle physicists' motivations for undertaking this bottom-up approach in the first place. Looking at EFTs from the perspective of modelling does not require taking a stance on some specific brand of realism or taking sides in the debate between reduction and emergence into which EFTs have recently been embedded. (shrink)

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.

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)

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)

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)

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)

In the April 2002 edition of JCS I outlined the conscious electromagnetic information field theory, claiming that consciousness is that component of the brain's electromagnetic field that is downloaded to motor neurons and is thereby capable of communicating its informational content to the outside world. In this paper I demonstrate that the theory is robust to criticisms. I further explore implications of the theory particularly as regards the relationship between electromagnetic fields, information, the phenomenology of (...) consciousness and the meaning of free will. Using cemi field theory I propose a working hypothesis that shows, among other things, that awareness and information represent the same phenomenon viewed from different reference frames. (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.

The theoretical physicist Paul Dirac rejected, explicitly on aesthetic grounds, a successful theory known as quantum electrodynamics (QED), which is the prototype for the family of theories known as quantum field theories (QFTs). Remarkably, the theoretical physicist Steven Weinberg, also largely on aesthetic grounds, supports QED and other QFTs. In order to evaluate these opposing aesthetic views a short introduction to the physical properties of QFTs is presented together with a detailed analysis of the aesthetic claims of Dirac (...) and Weinberg. It turns out that Dirac rejected QED, without regard to its success, because this theory fails to yield to what he perceived as beautiful mathematics, whereas Weinberg's support of QFTs is founded primarily on the physical concepts of the theories. In particular, he relies on symmetries that are the basis for the construction of the extremely successful current fundamental theories of particles physics. This success was decisive in leading to Weinberg's conviction of the beauty of QFTs. As a result of the evaluation of these approaches, the factors causing scientists to perceive a theory as being a fundamentally beautiful theory are discussed in detail. (shrink)

Free and weakly interacting particles are described by a second-quantized nonlinear Schrödinger equation, or relativistic versions of it. They describe Gaussian random walks with collisions. By contrast, the fields of strongly interacting particles are governed by effective actions, whose extremum yields fractional field equations. Their particle orbits perform universal Lévy walks with heavy tails, in which rare events are much more frequent than in Gaussian random walks. Such rare events are observed in exceptionally strong windgusts, monster or rogue waves, (...) earthquakes, and financial crashes. While earthquakes may destroy entire cities, the latter have the potential of devastating entire economies. (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)

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

Several theories of consciousness first described about a decade ago, including the conscious electromagnetic information (CEMI) field theory, claimed that the substrate of consciousness is the brain’s electromagnetic (EM) field. These theories were prompted by the observation, in many diverse systems, that synchronous neuronal firing, which generates coherent EM fields, was a strong correlate of attention, awareness, and consciousness. However, when these theories were first described there was no direct evidence that synchronous firing was actually functional, rather (...) than an epiphenomenon of brain function. Additionally, any EM field-based consciousness would be a ‘ghost in the machine’ unless the brain’s endogenous EM field is also able to influence neuron firing. Once again, when these theories were first described, there was only indirect evidence that the brain’s EM field influenced neuron firing patterns in the brain. In this paper I describe recent experimental evidence which demonstrate that synchronous neuronal firing does indeed have a functional role in the brain; and also that the brain’s endogenous EM field is involved in recruiting neurons to synchronously firing networks. The new data point to a new and unappreciated form of neural communication in the brain that is likely to have significance for all theories of consciousness. I describe an extension of the CEMI field theory that incorporates these recent experimental findings and integrates the theory with the ‘communication through coherence’ hypothesis. (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)

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)

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 structure of the classical spacetimes associated with such theories. This suggests that the intuitions that underlie the Received View are non-relativistic. Thus, to the extent that such intuitions are inappropriate in the relativistic context, they should be abandoned when it comes to interpreting RQFTs. (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.

In this chapter I examine seven clues to the nature of consciousness and explore what they reveal about the underlying physical substrate of consciousness. The consciousness clues are: it impacts upon the world; it is a property of living brains but no other structure; brain activity may be conscious or unconscious; the conscious mind appears to be serial; learning requires consciousness but recall doesn’t; conscious information is bound; and consciousness correlates with synchronous firing of neurons. I discuss field theories (...) of consciousness and introduce the conscious electromagnetic field (CEMI) theory that suggests that consciousness is a product of the brain’s electromagnetic field. I show that the CEMI field theory successfully accounts for each of the seven clues to the nature of consciousness. Finally, I show that although current quantum mechanical theories of consciousness are also field theories, they are physical untenable and should be discarded. (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)

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)

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering (...) the basics of the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by Doplicher, Haag, and Roberts (DHR); and we give an alternative proof of Doplicher and Robert's reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix. (shrink)

In this article we present a brief review of the conformal symmetry and the two-dimensional conformal quantum field theories. As concrete applications of the conformal theories to the critical phenomena in statistical systems, we calculate the value of central charge and the anomalous scale dimensions of the Z 2 symmetric quantum chain with boundary condition. The results are compatible with the prediction of the conformal field theories.

Quantum mechanics is a subject that has captured the imagination of a surprisingly broad range of thinkers, including many philosophers of science. Quantum field theory, however, is a subject that has been discussed mostly by physicists. This is the first book to present quantum field theory in a manner that makes it accessible to philosophers. Because it presents a lucid view of the theory and debates that surround the theory, An Interpretive Introduction to Quantum (...) Field Theory will interest students of physics as well as students of philosophy. -/- Paul Teller presents the basic ideas of quantum field theory in a way that is understandable to readers who are familiar with non-relativistic quantum mechanics. He provides information about the physics of the theory without calculational detail, and he enlightens readers on how to think about the theory physically. Along the way, he dismantles some popular myths and clarifies the novel ways in which quantum field theory is both a theory about fields and about particles. His goal is to raise questions about the philosophical implications of the theory and to offer some tentative interpretive views of his own. This provocative and thoughtful book challenges philosophers to extend their thinking beyond the realm of quantum mechanics and it challenges physicists to consider the philosophical issues that their explorations have encouraged. (shrink)

The somatic mutation theory (SMT) of cancer has been and remains the prevalent theory attempting to explain how neoplasms arise and progress. This theory proposes that cancer is a clonal, cell‐based disease, and implicitly assumes that quiescence is the default state of cells in multicellular organisms. The SMT has not been rigorously tested, and several lines of evidence raise questions that are not addressed by this theory. Herein, we propose experimental strategies that may validate the SMT. (...) We also call attention to an alternative theory of carcinogenesis, the tissue organization field theory (TOFT), which posits that cancer is a tissue‐based disease and that proliferation is the default state of all cells. Based on epistemological and experimental evidence, we argue that the TOFT compellingly explains carcinogenesis, while placing it within an evolutionarily relevant context.magnified imagemagnified imageAna Soto and Carlos Sonnenschein are at Tufts University School of Medicine, Boston, MA, USA. (shrink)

The author's version of the electromagnetic field theory of consciousness is stated briefly and then three difficulties with the theory are discussed. The first is a purely technical problem: how to measure accurately enough the spatial properties of the fields which are proposed to be conscious and then how to generate these artificially, so that the theory can be tested. The second difficulty might also be merely technical, or it might be substantive and fatal to the (...) theory. This is that present measurements seem to show a non-constant relationship between brain-generated electromagnetic fields and sensation. The third difficulty involves the basic question of whether consciousness per se has any direct effect on the brain. As an afterword, the disproportionate contribution of synchronously firing neurons to conscious percepts is simply explained in terms of the electromagnetic field theory of consciousness. Susan Pockett Difficulties with the Electromagnetic Field Theory of Consciousness: The author's version of the electromagnetic field theory of consciousness is stated briefly and then three difficulties with the theory are discussed. The first is a purely technical problem: how to measure accurately enough the spatial properties of the fields which are proposed to be conscious and then how to generate these artificially, so that the theory can be tested. The second difficulty might also be merely technical, or it might be substantive and fatal to the theory. This is that present measurements seem to show a non-constant relationship between brain-generated electromagnetic fields and sensation. The third difficulty involves the basic question of whether consciousness per se has any direct effect on the brain. As an afterword, the disproportionate contribution of synchronously firing neurons to conscious percepts is simply explained in terms of the electromagnetic field theory of consciousness. (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)

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.