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)

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 The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix.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)

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.

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)

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)

Approach to quantum field theory -- Scalar field theory -- Quantum electrodynamics -- Perspectives.

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)

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 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)

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)

In [3] John S. Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |Ψ|2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; such processes we call Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition (...) of the Markov processes, the efficient calculation of jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to “second quantization.” As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field. (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.

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)

Philosophical accounts of quantum theory commonly suppose that the observables of a quantum system form a Type-I factor von Neumann algebra. Such algebras always have atoms, which are minimal projection operators in the case of quantum mechanics. However, relativistic quantum field theory and the thermodynamic limit of quantum statistical mechanics make extensive use of von Neumann algebras of more general types. This chapter addresses the question whether interpretations of quantum probability devised (...) in the usual manner continue to apply in the more general setting. Features of non-type I factor von Neumann algebras are cataloged. It is shown that these novel features do not cause the familiar formalism of quantum probability to falter, since Gleason's Theorem and the Lüders Rule can be generalized. However, the features render the problem of the interpretation of quantum probability more intricate. (shrink)

The availability of unitarily inequivalent representations of the canonical commutation relations constituting a quantization of a classical field theory raises questions about how to formulate and pursue quantum field theory. In a minimally technical way, I explain how these questions arise and how advocates of the Hilbert space and of the algebraic approaches to quantum theory might answer them. Where these answers differ, I sketch considerations for and against each approach, as well as (...) considerations which might temper their apparent rivalry. (shrink)

Although philosophers have considered some of the implications of the nature of quantum statistics of many-particle systems for the interpretation problem, e.g., Reichenbach, they have not produced a complete analysis of the relationship between aspects of quantum statistics and complications and/or possible solutions of the interpretation problem. While the present work by no means provides a complete account, it does explore some heretofore uncharted regions. One of the latter is an analysis of a situation that I call 'The (...) Paradox of Identical Particles ,' which arises in Bose-Einstein statistics. PIP refers to the fact that Elementary Quantum Mechanics seems to be committed to the thesis that systems of particles of the same species, "identical" particles, exhibit behavior differing from that of systems of particles of different species, simply in virtue of the fact that the former contain entities of the same species while the latter do not. Taken at face value this is tantamount to the Empedoclean "axiom" that like attracts like, while like and unlike repel, a somewhat embarassingly naive proposition for modern physicists to embrace, and one which, furthermore, poses a host of perplexing problems, e.g., how do the particles "know" whether they are of the same species or not? A result proven in the present work is that any "pluralistic" interpretation of quantum theory is unable to provide a satisfactory way of ridding quantum physicists of this appeal to what I call "species sensitivity." Arguing that Quantum Field Theory is most naturally and plausibly interpreted as a "monistic" theory--which means, inter alia, that for a system of n identical particles to exist is not for n distinct objects of any kind to exist, but rather for one unified underlying entity, a quantum field, to be in a certain kind of state or condition--I show that from this point of view PIP can be dissolved. On the basis of this and other considerations, I argue that the interpretation problem is more amenable to solution if we take the QFT point of view as the fundamental expression of quantum 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.

The status of the vacuum in relativistic quantum field theory is examined. A sharp distinction arises between the global vacuum and the local vacuum. The concept of local number density is critically assessed. The global vacuum state implies fluctuations for all local observables. Correlations between such fluctuations in space-like separated regions of space-time are discussed and the existence of correlations which are maximal in a certain sense is remarked on, independently of how far apart those regions may (...) be. The analogy with the mirror-image correlations in the singlet state of two spin-1/2 particles is explained. The connection between these maximal correlations and the well-known violation of the Bell inequality in the vacuum state is discussed, together with the way in which the existence of these correlations might be exploited in developing a vacuum version of the Einstein-Podolsky-Rosen argument. The recent relativistic formulation of the Einstein-Podolsky-Rosen argument by Ghirardi and Grassi is critically assessed with particular reference to the vacuum case. (shrink)

An examination is made of the way in which particles emerge from linear, bosonic, massive quantum field theories. Two different constructions of the one-particle subspace of such theories are given, both illustrating the importance of the interplay between the quantum-mechanical linear structure and the classical one. Some comments are made on the Newton-Wigner representation of one-particle states, and on the relationship between the approach of this paper and those of Segal, and of Haag and Ruelle.

In this work, we attempt to define a notion of compositeness compatible with Quantum Field Theory. Considering the analytic properties of the S-matrix, we conclude that there is no satisfactory definition of compositeness compatible with Quantum Field Theory. Without this notion, one must claim that all bound states are equally fundamental, that is, one cannot rigorously claim that everyday objects are made of atoms or that atoms are made of protons and neutrons. I then (...) show how an approximate notion of compositeness may be recovered in the regime where the mass of a bound state is close to a multi-particle threshold. -/- Finally, we see that rejecting compositeness solves several of the "problems of everyday objects" encountered in an undergraduate metaphysics course. (shrink)

There are significant problems involved in determining the ontology of quantum field theory. An ontology involving particles seems to be ruled out due to the problem of defining localized position operators, issues involving interactions in QFT, and, perhaps, the appearance of unitarily inequivalent representations. While this might imply that fields are the most natural ontology for QFT, the wavefunctional interpretation of QFT has significant drawbacks. A modified field ontology is examined where determinables are assigned to open (...) bounded regions of spacetime instead of spacetime points. (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)

If the general arguments concerning the involvement of variation and selection in explanations of “fit” are valid, then variation and selection explanations should be appropriate, or at least potentially appropriate, outside the paradigm historistic domains of biology and knowledge. In this discussion, I wish to indicate some potential roles for variation and selection in foundational physics – specifically in quantum field theory. I will not be attempting any full coherent ontology for quantum field theory (...) – none currently exists, and none is likely for at least the short term future. Instead, I wish to engage in some partially speculative interpretations of some interesting results in this area with the aim of demonstrating that variation and selection notions might play a role even here. If variation and selection can survive in even as inhospitable and non-paradigmatic a terrain as foundational physics, then it can survive anywhere. (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)

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)

Alfred North Whitehead in his book Process and Reality describes the history of the universe in terms of a process of ‘creative advance into novelty.’ This advance is produced by a collection of happenings called ‘actual occasions’, or ‘actual entities’. Each actual entity has an associated actual world, and it arises from its own peculiar actual world. (PR 284). Two occasions are termed ‘contemporary’ if neither lies in the actual world of the other. A key issue is whether the words (...) in Process and Reality commit Whitehead to the relativity-theory idea that, at least in our present epoch, the creative advance into novelty is not serially ordered, or whether, alternatively, the logical developments in Part IV entail, at a deep metaphysical level, that the facts specified by two contemporary occasions become fixed and settled in some definite order. Irresolution on this basic question renders Whitehead’s theory obscure and plagued with controversy. I argue, in opposition to another paper in this issue, that Whitehead endorses the relativistic viewpoint, and consistently adheres to it. This makes Whitehead’s theory compatible with relativistic quantum theory. Combining Whitehead’s relativistic process theory with relativistic quantum field theory is therefore possible, and it holds the promise of producing a rationally coherent understanding far richer than what is provided by either theory alone of the relationships between the physically described aspects of the universe and human knowledge and intentions. (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)

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)

Quantum field theory provides the framework for many fundamental theories in modern physics, and over the last few years there has been growing interest in its historical and philosophical foundations. This anthology on the foundations of QFT brings together 15 essays by well-known researchers in physics, the philosophy of physics, and analytic philosophy.Many of these essays were first presented as papers at the conference?Ontological Aspects of Quantum Field Theory?, held at the Zentrum fr interdisziplin„re (...) Forschung, Bielefeld, Germany. The essays contain cutting-edge work on ontological aspects of QFT, including: the role of measurement and experimental evidence, corpuscular versus field-theoretic interpretations of QFT, the interpretation of gauge symmetry, and localization.This book is ideally suited to anyone with an interest in the foundations of quantum physics, including physicists, philosophers and historians of physics, as well as general readers interested in philosophy or science. (shrink)

Primitive ontology is a recently much discussed approach to the ontology of quantum theory according to which the theory is ultimately about entities in 3-dimensional space and their temporal evolution. This paper critically discusses the primitive ontologies that have been suggested within the Bohmian approach to quantum field theory in the light of the existence of unitarily inequivalent representations. These primitive ontologies rely either on a Fock space representation or a wave functional representation, which (...) are strictly speaking unambiguously available only for free systems in flat spacetime. As a consequence, it is argued that they do not constitute fundamental ontologies for quantum field theory, in contrast to the case of the Bohmian approach to quantum mechanics. (shrink)

This article explores the relationships between the philosophical foundations of quantum field theory, the currently dominant form of quantum physics, and Deleuze's concept of the virtual, most especially in relation to the idea of chaos found in Deleuze and Guattari's What is Philosophy?. Deleuze and Guattari appear to derive this idea partly from the philosophical conceptuality of quantum field theory, in particular the concept of virtual particle formation. The article then goes on to (...) discuss, from this perspective, the relationships between philosophy and science, and between their respective ways of confronting chaos, a great enemy but also a great friend of thought, and its greatest ally in its struggle against opinion. (shrink)

We propose a Quantum Field Theory description of beams on a Mach–Zehnder interferometer and apply the method to describe Interaction Free Measurements, concluding that there is a change of momentum of the fields in IFMs. Analysing the factors involved in the probability of emission of low-energy photons, we argue that they do not yield meaningful contributions to the probabilities of the IFMs.

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)

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)

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)

The physical, mathematical, and philosophical foundations of the quantum theory of free Bose fields in fixed general relativistic spacetimes are examined. It is argued that the theory is logically and mathematically consistent whereas semiclassical prescriptions for incorporating the back-reaction of the quantum field on the geometry lead to inconsistencies. Still, the relations and heuristic value of the semiclassical approach to canonical and covariant schemes of quantum gravity-plus-matter are assessed. Both conventional and rigorous formulations of (...) the theory and of its principal predictions, cosmological particle creation and horizon radiation, are expounded and compared. Special attention is devoted to spacetime properties needed for the existence or uniqueness of the relevant theoretical elements , renormalization of the stress tensor). The emergence of unitarily inequivalent representations in a single dynamical context is used as motivation for the introduction of the abstract $\rm C\sp{\*}$-algebraic axiomatic formalism. The operationalist and conventionalist claims of the original abstract algebraic program are criticized in favor of its tempered outgrowth, local quantum physics. The interpretation of the theory as a wave mechanics of classical field configurations, deriving from the Schrodinger representations of the abstract algebra, is discussed and is found superior, at least on the level of analogy, to particle or harmonic oscillator interpretations. Further, it is argued that the various detector results and the Fulling nonuniqueness problem do not undermine the particle concept in the ways commonly claimed. In particular, arguments are offered against the attribution of particle status to the Rindler quanta, against the physical realizability of the Rindler vacuum, and against the more general notion of observer-dependence as to the definition of 'particle' or 'vacuum'. However, the question of the ontological status of particles is raised in terms of the consistency of quantum field theory with non-reductive realism about particles, the latter being conceived as entities exhibiting attributes of discreteness and localizability. Two arguments against non-reductive realism about particles, one from axiomatic algebraic local quantum theory in Minkowski spacetime and one from quantum field theory in curved spacetime, are developed. (shrink)

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)

AUTHOR: STAN GUDDER (John Evans Professor of Mathematical Physics, University of Denver, USA) -- -/- We consider a discrete scalar, quantum field theory based on a cubic 4-dimensional lattice. We mainly investigate a discrete scattering operator S(x0,r) where x0 and r are positive integers representing time and maximal total energy, respectively. The operator S(x0,r) is used to define transition amplitudes which are then employed to compute transition probabilities. These probabilities are conditioned on the time-energy (x0,r). In order (...) to maintain total unit probability, the transition probabilities need to be reconditioned at each (x0,r). This is roughly analogous to renormalization in standard quantum field theory, except no infinities or singularities are involved. We illustrate this theory with a simple scattering experiment involving a common interaction Hamiltonian. We briefly mention how discreteness of space-time might be tested astronomically. Moreover, these tests may explain the existence of dark energy and dark matter. (shrink)

I derive a number of impressive analogies between the modifications of the elementary components of Matter, generated by an external source of interaction, and the analogous modifications of the elementary components of an Organism. I will consider the interaction between the elementary components of matter and a weak classic magnetic field. This interaction will be treated in the theoretical quantum field theory formalism.

I examine some problems standing in the way of a successful `field interpretation' of quantum field theory. The most popular extant proposal depends on the Hilbert space of `wavefunctionals.' But since wavefunctional space is unitarily equivalent to many-particle Fock space, two of the most powerful arguments against particle interpretations also undermine this form of field interpretation. IntroductionField Interpretations and Field OperatorsThe Wavefunctional InterpretationFields and Inequivalent Representations 4.1. The Rindler representation 4.2. Spontaneous symmetry breaking 4.3. (...) Coherent representations The Fate of Fields in Interacting QFTConclusions. (shrink)