Philosophers of quantum mechanics have generally addressed exceedingly simple systems. Laura Ruetsche offers a much-needed study of the interpretation of more complicated systems, and an underexplored family of physical theories, such as quantum field theory and quantum statistical mechanics, showing why they repay philosophical attention. She guides those familiar with the philosophy of ordinary QM into the philosophy of 'QM infinity', by presenting accessible introductions to relevant technical notions and the foundational questions they frame--and then develops and defends answers to (...) some of those questions. Finally, Ruetsche highlights ties between the foundational investigation of QM infinity and philosophy more broadly construed, in particular by using the interpretive problems discussed to motivate new ways to think about the nature of physical possibility and the problem of scientific realism. (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)

I argue against the currently prevalent view that algebraic quantum field theory (AQFT) is the correct framework for philosophy of quantum field theory and that “conventional” quantum field theory (CQFT), of the sort used in mainstream particle physics, is not suitable for foundational study. In doing so, I defend that position that AQFT and CQFT should be understood as rival programs to resolve the mathematical and physical pathologies of renormalization theory, and that CQFT has succeeded in this task and AQFT (...) has failed. I also defend CQFT from recent criticisms made by Doreen Fraser. (shrink)

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 give a fairly systematic and thorough presentation of the case for regarding black holes as thermodynamic systems in the fullest sense, aimed at students and non-specialists and not presuming advanced knowledge of quantum gravity. I pay particular attention to the availability in classical black hole thermodynamics of a well-defined notion of adiabatic intervention; the power of the membrane paradigm to make black hole thermodynamics precise and to extend it to local-equilibrium contexts; the central role of Hawking radiation in permitting (...) black holes to be in thermal contact with one another; the wide range of routes by which Hawking radiation can be derived and its back-reaction on the black hole calculated; the interpretation of Hawking radiation close to the black hole as a gravitationally bound thermal atmosphere. In an appendix I discuss recent criticisms of black hole thermodynamics by Dougherty and Callender. This paper confines its attention to the thermodynamics of black holes; a sequel will consider their statistical mechanics. (shrink)

Given its importance in modern physics, philosophers of science have paid surprisingly little attention to the subject of symmetries and invariances, and they have largely neglected the subtopic of symmetry breaking. I illustrate how the topic of laws and symmetries brings into fruitful interaction technical issues in physics and mathematics with both methodological issues in philosophy of science, such as the status of laws of physics, and metaphysical issues, such as the nature of objectivity.

`Quantum theory' is not a single physical theory but a framework in which many different concrete theories fit. As such, a solution to the quantum measurement problem ought to provide a recipe to interpret each such concrete theory, in a mutually consistent way. But with the exception of the Everett interpretation, the mainextant solutions either try to make sense of the abstract framework as if it were concrete, or else interpret one particular quantum theory under the fiction that it is (...) fundamental and exact. In either case, these approaches are unable to help themselves to the very theory-laden, level-relative ways in which quantum theory makes contact with experiment in mainstream physics, and so are committed to major revisionary projects which have not been carried out even in outline. As such, only the Everett interpretation is currently suited to make sense of quantum physics as we find it. (shrink)

Further arguments are offered in defence of the position that the variant of quantum field theory (QFT) that should be subject to interpretation and foundational analysis is axiomatic quantum field theory. I argue that the successful application of renormalization group (RG) methods within alternative formulations of QFT illuminates the empirical content of QFT, but not the theoretical content. RG methods corroborate the point of view that QFT is a case of the underdetermination of theory by empirical evidence. I also urge (...) caution in extrapolating interpretive conclusions about QFT from the application of RG methods in other contexts (e.g., condensed matter physics). This paper replies to criticisms advanced by David Wallace, but aims to be self-contained. (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)

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 mechanics, and classical mechanics, are framework theories that incorporate many different concrete theories which in general cannot be arranged in a neat hierarchy, but discussion of ‘the ontology of quantum mechanics’ tends to proceed as if quantum mechanics were a single concrete theory, specifically the physics of nonrelativistically moving point particles interacting by long-range forces. I survey the problems this causes and make some suggestions for how a more physically realistic perspective ought to influence the metaphysics of quantum mechanics.

I present in detail the case for regarding black hole thermodynamics as having a statistical-mechanical explanation in exact parallel with the statistical-mechanical explanation believed to underly the thermodynamics of other systems. I focus on three lines of argument: zero-loop and one-loop calculations in quantum general relativity understood as a quantum field theory, using the path-integral formalism; calculations in string theory of the leading-order terms, higher-derivative corrections, and quantum corrections, in the black hole entropy formula for extremal and near-extremal black holes; (...) recovery of the qualitative and quantitative structure of black hole statistical mechanics via the AdS/CFT correspondence. In each case I briefly review the content of, and arguments for, the form of quantum gravity being used at a introductory level: the paper is aimed at students and non-specialists and does not presume advanced knowledge of quantum gravity.. My conclusion is that the evidence for black hole statistical mechanics is as solid as we could reasonably expect it to be in the absence of a directly-empirically-verified theory of quantum gravity. (shrink)

Stephen Hawking has argued that universes containing evaporating black holes can evolve from pure initial states to mixed final ones. Such evolution is non-unitary and so contravenes fundamental quantum principles on which Hawking's analysis was based. It disables the retrodiction of the universe's initial state from its final one, and portends the time-asymmetry of quantum gravity. Small wonder that Hawking's paradox has met with considerable resistance. Here we use a simple result for C*-algebras to offer an argument for pure-to-mixed state (...) evolution in black hole evaporation, and review responses to the Hawking paradox with respect to how effectively they rebut this argument. (shrink)

The nature of antimatter is examined in the context of algebraic quantum field theory. It is shown that the notion of antimatter is more general than that of antiparticles. Properly speaking, then, antimatter is not matter made up of antiparticles—rather, antiparticles are particles made up of antimatter. We go on to discuss whether the notion of antimatter is itself completely general in quantum field theory. Does the matter–antimatter distinction apply to all field theoretic systems? The answer depends on which of (...) several possible criteria we should impose on the space of physical states. (shrink)

The Higgs mechanism gives mass to Yang-Mills gauge bosons. According to the conventional wisdom, this happens through the spontaneous breaking of gauge symmetry. Yet, gauge symmetries merely reflect a redundancy in the state description and therefore the spontaneous breaking can not be an essential ingredient. Indeed, as already shown by Higgs and Kibble, the mechanism can be explained in terms of gauge invariant variables, without invoking spontaneous symmetry breaking. In this paper, we present a general discussion of such gauge invariant (...) treatments for the case of the Abelian Higgs model, in the context of classical field theory. We thereby distinguish between two different notions of gauge: one that takes all local transformations to be gauge and one that relates gauge to a failure of determinism. (shrink)

A systematic analysis is made of the relations between the symmetries of a classical field and the symmetries of the one-particle quantum system that results from quantizing that field in regimes where interactions are weak. The results are applied to gain a greater insight into the phenomenon of antimatter.

An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the (...) stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories. (shrink)

The paper investigates the spontaneous breaking of gauge symmetries in gauge theories from a philosophical angle, taking into account the fact that the notion of a spontaneously broken local gauge symmetry, though widely employed in textbook expositions of the Higgs mechanism, is not supported by our leading theoretical frameworks of gauge quantum theories. In the context of lattice gauge theory, the statement that local gauge symmetry cannot be spontaneously broken can even be made rigorous in the form of Elitzur’s theorem. (...) Nevertheless, gauge symmetry breaking does occur in gauge quantum field theories in the form of the breaking of remnant subgroups of the original local gauge group under which the theories typically remain invariant after gauge fixing. The paper discusses the relation between these instances of symmetry breaking and phase transitions and draws some more general conclusions for the philosophical interpretation of gauge symmetries and their breaking. (shrink)

If we divide our physical theories into theories of matter and theories of spacetime, quantum field theory is our most fundamental empirically successful theory of matter. As such, it has attracted increasing attention from philosophers over the past two decades, beginning to eclipse its predecessor theory of quantum mechanics in the philosophical literature. Here I survey some central philosophical puzzles about the theory's foundations.

I distinguish two types of reduction within the context of quantum-classical relations, which I designate “formal” and “empirical”. Formal reduction holds or fails to hold solely by virtue of the mathematical relationship between two theories; it is therefore a two-place, a priori relation between theories. Empirical reduction requires one theory to encompass the range of physical behaviors that are well-modeled in another theory; in a certain sense, it is a three-place, a posteriori relation connecting the theories and the domain of (...) physical reality that both serve to describe. Focusing on the relationship between classical and quantum mechanics, I argue that while certain formal results concerning singular \ limits have been taken to preclude the possibility of reduction between these theories, such results at most provide support for the claim that singular limits block reduction in the formal sense; little if any reason has been given for thinking that they block reduction in the empirical sense. I then briefly outline a strategy for empirical reduction that is suggested by work on decoherence theory, arguing that this sort of account remains a fully viable route to the empirical reduction of classical to quantum mechanics and is unaffected by such singular limits. (shrink)

I argue that the metaphysical import of the Aharonov-Bohm effect has been overstated: correctly understood, it does not require either rejection of gauge invariance or any novel form of nonlocality. The conclusion that it does require one or the other follows from a failure to keep track, in the analysis, of the complex scalar field to which the magnetic vector potential is coupled. Once this is recognised, the way is clear to a local account of the ontology of electrodynamics ; (...) I sketch a possible such account. (shrink)

Quantum theory plays an increasingly significant role in contemporary early-universe cosmology, most notably in the inflationary origins of the fluctuation spectrum of the microwave background radiation. I consider the two main strategies for interpreting standard quantum mechanics in the light of cosmology. I argue that the conceptual difficulties of the approaches based around an irreducible role for measurement - already very severe - become intolerable in a cosmological context, whereas the approach based around Everett's original idea of treating quantum systems (...) as closed systems handles cosmological quantum theory satisfactorily. Contemporary cosmology, which indeed applies standard quantum theory without supplementation or modification, is thus committed - tacitly or explictly - to the Everett interpretation. (shrink)