I discuss issues concerning the philosophical foundations andimplications of quantum field theory, renormalization inparticular. A new understanding of the correspondence principle,an unexpected role of perturbation theory and, most of all, acriterion to reduce the set of consistent theories frominfinitely many to finitely many, are the key concepts of atheoretical set-up that appears to overcome in a natural wayvarious consistency problems of quantum mechanics and offerseveral hints for further developments.

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)

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)

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 manyparticle Fock space, two of the most powerful arguments against particle interpretations also undermine this form of field interpretation.

A resolution of the quantum measurement problem would require one to explain how it is that we end up with determinate records at the end of our measurements. Metaphysical commitments typically do real work in such an explanation. Indeed, one should not be satisfied with one's metaphysical commitments unless one can provide some account of determinate measurement records. I will explain some of the problems in getting determinate records in relativistic quantum field theory and pay particular attention to the relationship (...) between the measurement problem and a generalized version of Malament's theorem. (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)

Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum field theory (AQFT) provides a rigorous framework within which to analyse entanglement in the context of a fully relativistic formulation of quantum theory. What emerges from the analysis are new practical and theoretical limitations on an experimenter's ability to (...) perform operations on a field in one spacetime region that can disentangle its state from the state of the field in other spacelike-separated regions. These limitations show just how deeply entrenched entanglement is in relativistic quantum field theory, and yield a fresh perspective on the ways in which the theory differs conceptually from both standard non-relativistic quantum theory and classical relativistic field theory. (shrink)

Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the ‘reality’ of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e. inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a (...) particle is, and how a ‘particle’ will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the very same region of spacetime. We shall defend the idea that these representations provide complementary descriptions of the same state of the field against the claim that they embody completely incommensurable theories of the field. (shrink)

Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the "reality" of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e., inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a (...) particle is, and how a "particle" will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the *very same* region of spacetime. We shall defend the idea that these representations provide *complementary descriptions* of the same state of the field against the claim that they embody completely *incommensurable theories* of the field. (shrink)

In relativistic quantum field theory the notion of a local operation is regarded as basic: each open space-time region is associated with an algebra of observables representing possible measurements performed within this region. It is much more difficult to accommodate the notions of events taking place in such regions or of localized objects. But how can the notion of a local operation be basic in the theory if this same theory would not be able to represent localized measuring devices and (...) localized events? After briefly reviewing these difficulties we discuss a strategy for eliminating the tension, namely by interpreting quantum theory in a realist way. To implement this strategy we use the ideas of the modal interpretation of quantum mechanics. We then consider the question of whether the resulting scheme can be made Lorentz invariant. (shrink)

Although the philosophical literature on the foundations of quantum field theory recognizes the importance of Haag’s theorem, it does not provide a clear discussion of the meaning of this theorem. The goal of this paper is to make up for this deficit. In particular, it aims to set out the implications of Haag’s theorem for scattering theory, the interaction picture, the use of non-Fock representations in describing interacting fields, and the choice among the plethora of the unitarily inequivalent representations of (...) the canonical commutation relations for free and interacting fields. (shrink)

Although the philosophical literature on the foundations of quantum field theory recognizes the importance of Haag's theorem, it does not provide a clear discussion of the meaning of this theorem. The goal of this paper is to make up for this deficit. In particular, it aims to set out the implications of Haag's theorem for scattering theory, the interaction picture, the use of non-Fock representations in describing interacting fields, and the choice among the plethora of the unitarily inequivalent representations of (...) the canonical commutation relations for free and interacting fields. (shrink)

Quantum field theory (QFT) presents a genuine example of the underdetermination of theory by empirical evidence. There are variants of QFT—for example, the standard textbook formulation and the rigorous axiomatic formulation—that are empirically indistinguishable yet support different interpretations. This case is of particular interest to philosophers of physics because, before the philosophical work of interpreting QFT can proceed, the question of which variant should be subject to interpretation must be settled. New arguments are offered for basing the interpretation of QFT (...) on a rigorous axiomatic variant of the theory. The pivotal considerations are the roles that consistency and idealization play in this case. *Received June 2009; revised August 2009. †To contact the author, please write to: Department of Philosophy, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada; e‐mail: dlfraser@uwaterloo.ca. (shrink)

The CPT theorem of quantum field theory states that any relativistic (Lorentz-invariant) quantum field theory must also be invariant under CPT, the composition of charge conjugation, parity reversal and time reversal. This paper sketches a puzzle that seems to arise when one puts the existence of this sort of theorem alongside a standard way of thinking about symmetries, according to which spacetime symmetries (at any rate) are associated with features of the spacetime structure. The puzzle is, roughly, that the existence (...) of a CPT theorem seems to show that it is not possible for a well-formulated theory that does not make use of a preferred frame or foliation to make use of a temporal orientation. Since a manifold with only a Lorentzian metric can be temporally orientable—capable of admitting a temporal orientation—this seems to be an odd sort of necessary connection between distinct existences. The paper then suggests a solution to the puzzle: it is suggested that the CPT theorem arises because temporal orientation is unlike other pieces of spacetime structure, in that one cannot represent it by a tensor field. To avoid irrelevant technical details, the discussion is carried out in the setting of classical field theory, using a little-known classical analog of the CPT theorem. Introduction The Connection between Dynamical Symmetries and Spacetime Structure A Puzzle about the CPT Theorem A Classical PT Theorem 4.1 Bell's theorem 4.2 Auxiliary constraints Resolution of the Puzzle Galilean-Invariant Field Theories 6.1 Temporal orientation in Galilean spacetime 6.2 Counterexample to the Galilean PT hypothesis Conclusions CiteULike Connotea Del.icio.us What's this? (shrink)

This dissertation reconsiders some traditional issues in the foundations of quantum mechanics in the context of relativistic quantum field theory (RQFT); and it considers some novel foundational issues that arise first in the context of RQFT. The first part of the dissertation considers quantum nonlocality in RQFT. Here I show that the generic state of RQFT displays Bell correlations relative to measurements performed in any pair of spacelike separated regions, no matter how distant. I also show that local systems in (...) RQFT are "open" to influence from their environment, in the sense that it is generally impossible to perform local operations that would remove the entanglement between a local system and any other spacelike separated system. The second part of the dissertation argues that RQFT does not support a particle ontology -- at least if particles are understood to be localizable objects. In particular, while RQFT permits us to describe situations in which a determinate number of particles are present, it does not permit us to speak of the location of any individual particle, nor of the number of particles in any particular region of space. Nonetheless, the absence of localizable particles in RQFT does not threaten the integrity of our commonsense concept of a localized object. Indeed, RQFT itself predicts that descriptions in terms of localized objects can be quite accurate on the macroscopic level. The third part of the dissertation examines the so-called observer-dependence of the particle concept in RQFT -- that is, whether there are any particles present must be relativized to an observer's state of motion. Now, it is not uncommon for modern physical theories to subsume observer-dependent descriptions under a more general observer-independent description of some underlying state of affairs. However, I show that the conflicting accounts concerning the particle content of the field cannot be reconciled in this way. In fact, I argue that these conflicting accounts should be thought of as "complementary" in the same sense that position and momentum descriptions are complementary in elementary quantum mechanics. (shrink)

Many of the "counterintuitive" features of relativistic quantum field theory have their formal root in the Reeh-Schlieder theorem, which in particular entails that local operations applied to the vacuum state can produce any state of the entire field. It is of great interest then that I.E. Segal and, more recently, G. Fleming (in a paper entitled "Reeh-Schlieder meets Newton-Wigner") have proposed an alternative "Newton-Wigner" localization scheme that avoids the Reeh-Schlieder theorem. In this paper, I reconstruct the Newton-Wigner localization scheme and (...) clarify the limited extent to which it avoids the counterintuitive consequences of the Reeh-Schlieder theorem. I also argue that there is no coherent interpretation of the Newton-Wigner localization scheme that renders it free from act-outcome correlations at spacelike separation. (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)

Static Maxwell-Einstein continuum mechanical gravitoelectromagnetic total stress energy momentum density tensor eigenvector matrix configuration space, provides flux for time dependent quantum mechanical eigenvalue matrix operator observables via Dirac-Noether conserved angular momentum probability current symmetry. Fundamental quantum continuum
equation returns eigenvalues of photon gravitoelectromagnetic spectrum in units of Maxwell stress tensor pascals. Energization of off-diagonal stress tensor components results in electron-positron (moment of inertia x angular velocity) angular momentum origin of particle wave mass charge eigenvalues. In thought experiment test vs. general (...) theory via pp-waves microlensing problem, where light-to-light gravitational attraction is four times matter-to-matter attraction, hypothesis predicts null result in area general theory known to break down on microscopic scale.
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This paper explores various functions of idealizations in quantum field theory. To this end it is important to first distinguish between different kinds of theories and models of or inspired by quantum field theory. Idealizations have pragmatic and cognitive functions. Analyzing a case-study from hadron physics, I demonstrate the virtues of studying highly idealized models for exploring the features of theories with an extremely rich structure such as quantum field theory and for gaining some understanding of the physical processes in (...) the system under consideration. (shrink)

In this paper I put forward a suggestion for identifying causality in micro-systems with the specific quantum field theoretic interactions that occur in such systems. I first argue — along the lines of general transference theories — that such a physicalistic account is essential to an understanding of causation; I then proceed to sketch the concept of interaction as it occurs in quantum field theory and I do so from both a formal and an informal point of view. Finally, I (...) present reasons for thinking that only a quantum field theoretic account can do the job — in particular I rely on a theorem by D. Currie and to the effect that interaction cannot be described in (a Hamiltonian formulation of) Classical Mechanics. Throughout the paper I attempt to suggest that the widespread scepticism about the ability of quantum theory to support a theory of causality is mistaken and rests on several misunderstandings. (shrink)

There are two opposing traditions in contemporary quantum field theory (QFT). Mainstream Lagrangian QFT led to and supports the standard model of particle interactions. Algebraic QFT seeks to provide a rigorous consistent mathematical foundation for field theory, but cannot accommodate the local gauge interactions of the standard model. Interested philosophers face a choice. They can accept algebraic QFT on the grounds of mathematical consistency and general accord with the semantic conception of theory interpretation. This suggests a rejection of particle ontology. (...) Or they can accept the standard model on the grounds of its established success. This alternative, which I defend, suggests revising philosophical accounts of scientific theory and finding some way of accommodating particles. *Received December 2005; accepted April 2008. †To contact the author, please write to: 2045 Manzanita Drive, Oakland, CA 94611; e‐mail: emackinnon@comcast.net. (shrink)

An epistemological interpretation of quantum mechanics hinges on the claim that the distinctive features of quantum mechanics can be derived from some distinctive features of an observational basis. Old and new variations of this theme are listed. The program has a limited success in non-relativistic quantum mechanics. The crucial issue is how far it can be extended to quantum field theory without introducing significant ontological postulates. A C*-formulation covers algebraic quantum field theory, but not the standard model. Julian Schwinger’s anabatic (...) methodology extended a strict measurement-based formulation of quantum mechanics through field theory. His extension also excluded the quark hypothesis and the standard model. Quarks and local gauge invariance are postulates that go beyond the limits of an epistemological interpretation of quantum mechanics. The ontological significance ascribed to these advances depends on the role accorded ontology. (shrink)

Philosophical interpretations of theories generally presuppose that a theory can be presented as a consistent mathematical formulation that is interpreted through models. Algebraic quantum field theory (AQFT) can fit this interpretative model. However, standard Lagrangian quantum field theory (LQFT), as well as quantum electrodynamics and nuclear physics, resists recasting along such formal lines. The difference has a distinct bearing on ontological issues. AQFT does not treat particle interactions or the standard model. This paper develops a framework and methodology for interpreting (...) such informal theories as LQFT and the standard model. We begin by summarizing two minimal epistemological interpretation of non-relativistic quantum mechanics (NRQM): Bohrian semantics, which focuses on communicables; and quantum information theory, which focuses on the algebra of local observables. Schwinger's development of quantum field theory supplies a unique path from NRQM to QFT, where each step is conceptually anchored in local measurements. LQFT and the standard model rely on postulates that go beyond the limits set by AQFT and Schwinger's anabatic methodology. The particle ontology of the standard model is clarified by regarding the standard model as an informal modular theory with a limited range of validity. (shrink)

Earman and Ruetsche ([1995]) have cast their gaze upon existing no-go theorems for relativistic modal interpretations, and have found them inconclusive. They suggest that it would be more fruitful to investigate modal interpretations proposed for ‘really relativistic theories,’ that is, algebraic relativistic quantum field theories. They investigate the proposal of (Clifton [2000]), and extend Clifton's result that, for a host of states, his proposal yields no definite observables other than multiples of the identity. This leads Earman and Ruetsche to a (...) suspicion that troubles for modal interpretations of such relativistic theories ‘are due less to the Poincaré invariance of relativistic QFT vs. the Galilean invariance of ordinary nonrelativistic QM than to the infinite number of degrees of freedom of former vs. the finite number of degrees of freedom of the latter’ (pp. 577–8). I am skeptical of this suggestion. Though there are troubles for modal interpretations of relativistic quantum field theory that are due to its being a field theory—that is, due to infinitude of the degrees of freedom—they are not the only troubles faced by modal interpretations of quantum theories set in relativistic spacetime; there are also troubles traceable to relativistic causal structure. (shrink)

If $\{{\cal A}(V)\}$ is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and $V_1$ and $V_2$ are spacelike separated spacetime regions, then the system $({\cal A}(V_1),{\cal A}(V_2),\phi)$ is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections $A\in{\cal A}(V_1)$, $B\in{\cal A}(V_2)$ correlated in the normal state $\phi$ there exists a projection $C$ belonging to a von Neumann algebra associated with a spacetime region $V$ contained in the (...) union of the backward light cones of $V_1$ and $V_2$ and disjoint from both $V_1$ and $V_2$, a projection having the properties of a Reichenbachian common cause of the correlation between $A$ and $B$. It is shown that if the net has the local primitive causality property then every local system $({\cal A}(V_1),{\cal A}(V_2),\phi)$ with a locally normal and locally faithful state $\phi$ and open bounded $V_1$ and $V_2$ satisfies the Weak Reichenbach's Common Cause Principle. (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.

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (QFT) (that is, the ‘naive’ (QFT) used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian (QFT) has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least (...) as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work. (shrink)

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the "naive" quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian (...) QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work. (shrink)

Nick Huggett and Robert Weingard (1994) have recently proposed a novel approach to interpreting field theories in physics, one which makes central use of the fact that a field generally has an infinite number of degrees of freedom in any finite region of space it occupies. Their characterization, they argue, (i) reproduces our intuitive categorizations of fields in the classical domain and thereby (ii) provides a basis for arguing that the quantum field is a field. Furthermore, (iii) it accomplishes these (...) tasks better than does a well-known rival approach due to Paul Teller (1990, 1995). This paper contends that all three of these claims are mistaken, and suggests that Huggett and Weingard have not shown how counting degrees of freedom provides any insight into the interpretation or the formal properties of field theories in physics. (shrink)