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

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.

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.

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.

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)

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 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)

Anglophone scholars with a postcolonial perspective have forcefully challenged eurocentric definitions of comparative literature and the limits of national frameworks. But this debate ‘offers few methodological solutions to the pragmatic issue of how to make credible comparisons among radically different languages and literatures’. Moreover, some have even rejected the very notion of comparison, impugning its association with nationalistic and imperialistic perspectives or its unsuitability for the study of historical, dynamic and multidimensional processes. This article offers a synthetic overview of the (...) tools field theory provides for literature studies in a global perspective without sacrificing methodological rigour and empirical validation. It discusses the epistemological principles set out in The Craft of Sociology to address problems of comparison; the possibility of rational dialogue between different theoretical frameworks; the properties which make Bourdieu's model more complete than other approaches to literary phenomena; and finally, developments of field theory and issues raised by globalization. (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)

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)

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)

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.

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)

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.

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)

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)

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)

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)

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)

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)

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.

I suggest that the current situation in quantum field theory (QFT) provides some reason to question the universal validity of ontological reductionism. I argue that the renormalization group flow is reversible except at fixed points, which makes the relation between large and small distance scales quite symmetric in QFT, opening up at least the technical possibility of a non-reductionist approach to QFT. I suggest that some conceptual problems encountered within QFT may potentially be mitigated by moving to an (...) alternative picture in which it is no longer the case that the large supervenes on the small. Finally, I explore some specific models in which a form of non-reductionism might be implemented, and consider the prospects for future development of these models. (shrink)

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)

In this article, I criticize available democracy consolidation theories for assuming that the ontology of political structure and elite subjectivity are based upon historically transcendent a priori principles. In contrast to this assumption, I adopt a political field theory perspective to argue that concepts for comprehending the politics behind democracy consolidation must be reconstructed based on the history of conflicts among political actors over the meaning of politics. I demonstrate the significance of this insight for comprehending politics by (...) empirically adopting it to explain the case of Emergency in India (1975–1977). Using Multiple Correspondence Analysis, network analysis, and content analysis of biographies of politicians elected for the 1971 Indian parliament, I demonstrate that the politics behind Emergency can be comprehended only when we take into account the history of conflict since the late colonial period between those leaders who insisted that Indian politics was defined by the network of ties among politicians and those who believed that Indian politics must reflect the aspirations of the masses. The main point of this article is that the ontological principles of current political structure, elite subjectivity, and political institutions are rooted within the chaotic history of conflict among leaders over the meaning of politics. (shrink)

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)

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)

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)

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)

Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using a simple thought experiment, that quantum theory follows from decompositional equivalence together with Landauer’s principle. This demonstration raises within physics a question previously left to psychology: how do human—or any—observers identify or agree about what constitutes a “system of interest”?

In this article, we demonstrate a sense in which the one-particle quantum mechanics and the classical electromagnetic four-potential arise from the quantum field theory. In addition, the classical Maxwell equations are derived from the QFT scattering process, while both classical electromagnetic fields and potentials serve as mathematical tools to approximate the interactions among elementary particles described by QFT physics. Furthermore, a plausible interpretation of the Aharonov–Bohm effect is raised within the QFT framework. We provide a quantum treatment of (...) the source of electromagnetic potentials and argue that the underlying mechanism in the AB effect can be understood via interactions among electrons described by QFT theory where the interactions are mediated by virtual photons. (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)

Relativistic mean field theory with mesons σ, ω, π and ρ mediating interactions and nucleons as basic fermions has been very successful in describing nuclear matter and finite nuclei. However, in heavy-ion collisions, where the c. m. energy of two colliding nucleons will be in the hundreds of GeV region, nucleons are not expected to behave as point-like particles. Analyses of elastic pp and ¯pp scattering data in the relevant c. m. energy range show that the nucleon is (...) a composite object—a topological soliton or Skyrmion embedded in a condensed quark-antiquark ground state. Against this backdrop, we formulate an effective field theory model of nuclear matter based on the gauged linear σ-model where quarks are the basic fermions, but the mesons still mediate the interactions. The model describes the nucleon as a Skyrmion and produces a q¯q ground state analogous to a superconducting ground state. Quarks are quasi-particles in this ground state. When the temperature exceeds a critical value, the scalar field in the ground state vanishes, quarks become massless, and a chiral phase transition occurs leading to chiral symmetry restoration. We explore the possibility of a first order phase transition in this model by introducing suitable self-interactions of the scalar field. Internal structures of the Skyrmions are ignored, and they are treated as point-like fermions. (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)