Ruetsche ([2011]) argues that the occurrence of unitarily inequivalent representations in quantum theories with infinitely many degrees of freedom poses a novel interpretational problem. According to Ruetsche, such theories compel us to reject the so-called ideal of pristine interpretation; she puts forward the ‘coalescence approach’ as an alternative. In this paper I offer a novel defence of the coalescence approach. The defence rests on the claim that the ideal of pristine interpretation already fails before one considers the (...) peculiarities of QM∞: there are pre-QM∞ parallels to coalescence. Despite this departure from pristinism, the ‘modest’ view that emerges poses no threat to scientific realism. (shrink)

We critically review the recent debate between Doreen Fraser and David Wallace on the interpretation of quantum field theory, with the aim of identifying where the core of the disagreement lies. We show that, despite appearances, their conflict does not concern the existence of particles or the occurrence of unitarily inequivalent representations. Instead, the dispute ultimately turns on the very definition of what a quantum field theory is. We further illustrate the fundamental differences between the two approaches (...) by comparing them both to the Bohmian program in quantum field theory. (shrink)

Ruetsche argues that a problem of unitarily inequivalent representations arises in quantum theories with infinitely many degrees of freedom. I provide an algebraic formulation of classical field theories and show that unitarily inequivalent representations arise there as well. I argue that the classical case helps us rule out one possible response to the problem of unitarily inequivalent representations called Hilbert Space Conservatism.

Howard argues that the existence of unitarily inequivalent representations in Quantum Field Theory presents a problem for structural realism in this context. I consider two potential ways round this problem: 1), follow Wallace in adopting the 'naive' Lagrangian form of QFT with cut-offs; 2), adapt Ruetsche's 'Swiss Army Knife' approach. The first takes us into the current debate between Wallace and Fraser on conventional vs. algebraic QFT. The second involves consideration of the role of inequivalent (...) class='Hi'>representations in understanding spontaneous symmetry breaking and quantum statistics. In both cases, I suggest, the structural realist has sufficient room to manoeuvre. (shrink)

We pose and resolve a puzzle about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator in a ground state's GNS representation. But Wigner's theorem guarantees that any symmetry's action on states is given by a unitary operator. How can this unitary operator fail to implement the symmetry in the GNS representation? We show how it is possible for a unitary operator of this (...) sort to connect the folia of unitarily inequivalent representations. This result undermines interpretations of quantum theory that hold unitary equivalence to be necessary for physical equivalence. (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)

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)

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)

It is shown that the automorphism group of a relation algebra ${\cal B}_P$ constructed from a projective geometry P is isomorphic to the collineation group of P. Also, the base automorphism group of a representation of ${\cal B}_P$ over an affine geometry D is isomorphic to the quotient of the collineation group of D by the dilatation subgroup. Consequently, the total number of inequivalent representations of ${\cal B}_P$ , for finite geometries P, is the sum of the numbers (...) ${\mid Col(P)\mid\over {\mid Col(D)\mid/\mid Dil(D)\mid}}$ where D ranges over a list of the non-isomorphic affine geometries having P as their geometry at infinity. This formula is used to compute the number of inequivalent representations of relation algebras constructed over projective lines of order at most 10. For instance, the relation algebra constructed over the projective line of order 9 has 56,700 mutually inequivalent representations. (shrink)

On standard accounts of scientific theorizing, the role of idealizations is to facilitate the analysis of some real world system by employing a simplified representation of the target system, raising the obvious worry about how reliable knowledge can be obtained from inaccurate descriptions. The idealizations involved in the Aharonov–Bohm effect do not, it is claimed, fit this paradigm; rather the target system is a fictional system characterized by features that, though physically possible, are not realized in the actual world. The (...) point of studying such a fictional system is to understand the foundations of quantum mechanics and how its predictions depart from those of classical mechanics. The original worry about the use of idealizations is replaced by a new one; namely, how can actual world experiments serve to confirm the AB effect if it concerns the behavior of a fictional system? Struggle with this issue helps to account for the fact that almost three decades elapsed before a consensus emerged that the predicted AB effect had received solid experimental support. Standard accounts of idealizations tout the role they play in making tractable the analysis of the target system; by contrast, the idealizations involved in the AB effect make its analysis both conceptually and mathematically challenging. The idealizations required for the AB effect are also responsible for the existence of unitarily inequivalent representations of the canonical commutation relations and of the current algebra, representations which an observer confined to the electron’s configuration space could invoke to ‘explain’ AB-type effect without the need to posit a hidden magnetic field. The goal of this paper is to bring to the attention of the philosophers of science these and other aspects of the AB effect which are neglected or inadequately treated in literature. (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)

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 (...) class='Hi'>inequivalent representations of the canonical commutation relations for free and interacting fields. (shrink)

On standard accounts of scientific theorizing, the role of idealizations is to facilitate the analysis of some real world system by employing a simplified representation of the target system, raising the obvious worry about how reliable knowledge can be obtained from inaccurate descriptions. The idealizations involved in the Aharonov–Bohm effect do not, it is claimed, fit this paradigm; rather the target system is a fictional system characterized by features that, though physically possible, are not realized in the actual world. The (...) point of studying such a fictional system is to understand the foundations of quantum mechanics and how its predictions depart from those of classical mechanics. The original worry about the use of idealizations is replaced by a new one; namely, how can actual world experiments serve to confirm the AB effect if it concerns the behavior of a fictional system? Struggle with this issue helps to account for the fact that almost three decades elapsed before a consensus emerged that the predicted AB effect had received solid experimental support. Standard accounts of idealizations tout the role they play in making tractable the analysis of the target system; by contrast, the idealizations involved in the AB effect make its analysis both conceptually and mathematically challenging. The idealizations required for the AB effect are also responsible for the existence of unitarily inequivalent representations of the canonical commutation relations and of the current algebra, representations which an observer confined to the electron’s configuration space could invoke to ‘explain’ AB-type effect without the need to posit a hidden magnetic field. The goal of this paper is to bring to the attention of the philosophers of science these and other aspects of the AB effect which are neglected or inadequately treated in literature. (shrink)

Some physicists and philosophers argue that unitarily inequivalent representations in quantum field theory are mathematical surplus structure. Support for that view, sometimes called ‘algebraic imperialism’, relies on Fell’s theorem and its deployment in the algebraic approach to QFT. The algebraic imperialist uses Fell’s theorem to argue that UIRs are ‘physically equivalent’ to each other. The mathematical, conceptual, and dynamical aspects of Fell’s theorem will be examined. Its use as a criterion for physical equivalence is examined in detail (...) and it is proven that Fell’s theorem does not apply to the vast number of representations used in the algebraic approach. UIRs are not another case of theoretical underdetermination, because they make different predictions about ‘classical’ operators. These results are applied to the Unruh effect where there is a continuum of UIRs to which Fell’s theorem does not apply. _1_ Introduction _2_ Weak Equivalence and Physical Equivalence _3_ Mathematical Overview of Algebraic Quantum Field Theory _4_ Fell’s Theorem and Philosophical Responses to Weak Equivalence _5_ Weak Equivalence in C*-Algebras and W*-Algebras _6_ Classical Equivalence and Weak Equivalence _7_ Interlude: Is Weak Equivalence Really Physical Equivalence? _8_ The Unruh Effect _9_ Time Evolution and Symmetries _10_ Conclusions Appendix. (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)

This unpublished paper, written in 2005 in the PhD philosophy program at Notre Dame, argues that algebraic structural realism faces a difficulty raised by the existence of inequivalent representations in quantum field theory.

Many philosophical and scientific discussions of topics of mind-matter research make implicit assumptions, in various guises, about the distinction between mind and matter. Currently predominant positions are based on either reduction or emergence, providing either monistic or dualistic scenarios. A more-involved framework of thinking, which can be traced back to Spinoza and Leibniz, combines the two scenarios, dualistic (with mind and matter separated) and monistic (with mind and matter unseparated), in one single picture. Based on such a picture, the transition (...) from a domain with mind and matter unseparated to separate mental and material domains can be viewed as a result of a general kind of symmetry breaking, which can be described formally in terms of inequivalent representations. The possibility of whether this symmetry breaking might be connected to the emergence of temporal directions from temporally non-directed or even non-temporal levels of reality will be discussed. Correlations between mental and material aspects of reality could then be imagined as remnants of such primordial levels. Different conceivable types of inequivalent representations would lead to correlations with different characteristics. (shrink)

body. While the latter areas are discussed mainly in fields such as the philosophy of mind, cognitive Many philosophical and scientific discussions of top-.

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)

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)

The difficulties of relativistic particle theories formulated by means of canonical quantization, such as those of Klein–Gordon and Dirac, ultimately led theoretical physicists to turn to quantum field theory to model elementary particle physics. In order to overcome these difficulties, the theories of the present approach are developed deductively from the physical principles that specify the system, without making use of canonical quantization. For a free particle these starting assumptions are invariance of the theory and covariance of position with respect (...) to Poincaré transformations. In pursuing the approach, the effectiveness of group theoretical methods is exploited. The coherent development of our program has shown that robust classes of representations of the Poincaré group, discarded by the known particle theories, can in fact be taken as bases for perfectly consistent theories. For massive spin zero particles, six inequivalent theories have been determined, two of which do not correspond to any of the current ones; all of these theories overcome the difficulties of Klein–Gordon one. The present lack of the explicit transformation properties of position with respect to boosts prevents the complete determination of non zero spin particle theories. In the past a particular form of these transformation properties was adopted by Jordan and Mukunda. We check its consistency within the present approach and find that for spin \ particles there is only one consistent theory, which is unitarily related to Dirac’s; yet, once again, it requires classes of irreducible representations previously discarded. (shrink)

We point out that, when the dimension of the Hilbert space is greater than two, Bell’s operators entering the Bell-CHSH inequality do exhibit inequivalent unitary matrix representations. Although the Bell-CHSH inequality turns out to be violated, the size of the violation is different for different representations, the maximum violation being given by Tsirelson’s bound. The feature relies on a pairing mechanism between the modes of the Hilbert space of the system.

Taking the BCS Hamiltonian written in second-quantized form, a modified form of Umezawa's self-consistent field theory method is applied, and a unitarily nonequivalent representation is selected in which the Hamiltonian obviously describes a superconducting system. This result is not at all obvious, since the original Hamiltonian is completely symmetric, and there is no reason a priori for expecting it to describe an asymmetric superconducting configuration. All higher order terms are accounted for, and in doing so, one finds the existence (...) of the energy-gap condition for Cooper pairs. The representation is picked out without using the adiabatic theorem or pair approximation, as is typically done in the self-consistent method for superconductivity. (shrink)

We discuss the intertwined topics of Fulling non‐uniqueness and the Unruh effect. The Fulling quantization, which is in some sense the natural one for an observer uniformly accelerated through Minkowski spacetime to adopt, is often heralded as a quantization of the Klein‐Gordon field which is both physically relevant and unitarily inequivalent to the standard Minkowski quantization. We argue that the Fulling and Minkowski quantizations do not constitute a satisfactory example of physically relevant, unitarily inequivalent quantizations, and (...) indicate what it would take to settle the open question of whether a satisfactory example exists. A popular gloss on the Unruh effect has it that an observer uniformly accelerated through the Minkowski vacuum experiences a thermal flux of Rindler quanta. Taking the Unruh effect, so glossed, to establish that the notion of particle must be relativized to a reference frame, some would use it to demote the particle concept from fundamental status. We explain why technical results do not support the popular gloss and why the attempted demotion of the particle concept is both unsuccessful and unnecessary. Fulling non‐uniqueness and the Unruh effect merit attention despite these negative verdicts because they provide excellent vehicles for illustrating key concepts of quantum field theory and for probing foundational issues of considerable philosophical interest. (shrink)

We discuss the intertwined topics of Fulling non-uniqueness and the Unruh effect. The Fulling quantization, which is in some sense the natural one for an observer uniformly accelerated through Minkowski spacetime to adopt, is often heralded as a quantization of the Klein-Gordon field which is both physically relevant and unitarily inequivalent to the standard Minkowski quantization. We argue that the Fulling and Minkowski quantizations do not constitute a satisfactory example of physically relevant, unitarily inequivalent quantizations, and (...) indicate what it would take to settle the open question of whether a satisfactory example exists. A popular gloss on the Unruh effect has it that an observer uniformly accelerated through the Minkowski vacuum experiences a thermal flux of Rindler quanta. Taking the Unruh effect, so glossed, to establish that the notion of particle must be relativized to a reference frame, some would use it to demote the particle concept from fundamental status. We explain why technical results do not support the popular gloss and why the attempted demotion of the particle concept is both unsuccessful and unnecessary. Fulling non-uniqueness and the Unruh effect merit attention despite these negative verdicts because they provide excellent vehicles for illustrating key concepts of quantum field theory and for probing foundational issues of considerable philosophical interest. (shrink)

It is shown that the 33 complex rays in three dimensions used by Penrose to prove the Bell-Kochen-Specker theorem have the same orthogonality relations as the 33 real rays of Peres, and therefore provide an isomorphic proof of the theorem. It is further shown that the Peres and Penrose rays are just two members of a continuous three-parameter family of unitarily inequivalent rays that prove the theorem.

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)

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)

The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the problem solver, unitarily computes the corresponding solution and reads it by the final measurement. This simple extension creates a new perspective from which to see the quantum algorithm. First, it highlights the relevance of time-symmetric quantum mechanics to quantum computation: the problem-setting (...) and problem solution, in their quantum version, constitute pre- and post-selection, hence the process as a whole is bound to be affected by both boundary conditions. Second, it forces us to enter into relational quantum mechanics. There must be a representation of the quantum algorithm with respect to Bob, and another one with respect to Alice, from whom the outcome of the initial measurement, specifying the setting and thus the solution of the problem, must be concealed. Time-symmetrizing the quantum algorithm to take into account both boundary conditions leaves the representation to Bob unaltered. It shows that the representation to Alice is a sum over histories in each of which she remains shielded from the information coming to her from the initial measurement, not from that coming to her backwards in time from the final measurement. In retrospect, all is as if she knew in advance, before performing her problem-solving action, half of the information that specifies the solution of the problem she will read in the future and could use this information to reach the solution with fewer computation steps. This elucidates the quantum computational speedup in all the quantum algorithms examined. (shrink)

Earman and Norton argue that manifold realism leads to inequivalence of Leibniz-shifted space-time models, with undesirable consequences such as indeterminism. I respond that intrinsic axiomatization of space-time geometry shows the variant models to be isomorphic with respect to the physically meaningful geometric predicates, and therefore certainly physically equivalent because no theory can characterize its models more closely than this. The contrary philosophical arguments involve confusions about identity and representation of space-time points, fostered by extrinsic coordinate formulations and irrelevant modal metaphysics. (...) I conclude that neither the revived Einstein hole argument nor the original Leibniz indiscernibility argument have any force against manifold realism. (shrink)

A solution to the measurement problem of quantum mechanics is proposed within the framework of an intepretation according to which only quantum systems with an infinite number of degrees of freedom have determinate properties, i.e., determinate values for (some) observables of the theory. The important feature of the infinite case is the existence of many inequivalent irreducible Hilbert space representations of the algebra of observables, which leads, in effect, to a restriction on the superposition principle, and hence the (...) possibility of defining (macro-) observables which commute with every observable. Such observables have determinate values which are not subject to quantum interference effects. A measurement process is schematized as an interaction between a microsystem and a macrosystem, idealized as an infinite quantum system, and it is shown that there exists a unitary transformation which transforms the initial pure state of the composite system in a finite time (the duration of the interaction) into the required mixture of disjoint states. (shrink)

Framing effects occur when people respond differently to the same information, just because it is conveyed in different words. For example, in the classic ‘Disease Problem’ introduced by Amos Tversky and Daniel Kahneman, people’s choices between alternative interventions depend on whether these are described positively, in terms of the number of people who will be saved, or negatively in terms of the corresponding number who will die. In this paper, I discuss an account of framing effects based on ‘fuzzy-trace theory’. (...) The central claim of this account is that people represent the numbers in framing problems in a ‘gist-like’ way, as ‘some’; and that this creates a categorical contrast between ‘some’ people being saved (or dying) and ‘no’ people being saved (or dying). I argue that fuzzy-trace theory’s gist-like representation, ‘some’, must have the semantics of ‘some and possibly all’, not ‘some but not all’. I show how this commits fuzzy-trace theory to a modest version of a rival ‘lower bounding hypothesis’, according to which lower-bounded interpretations of quantities contribute to framing effects by rendering the alternative descriptions extensionally inequivalent. As a result, fuzzy-trace theory is incoherent as it stands. Making sense of it requires dropping, or refining, the claim that decision-makers perceive alternatively framed options as extensionally equivalent; and the related claim that framing effects are irrational. I end by suggesting that, whereas the modest lower bounding hypothesis is well supported, there is currently less evidence for the core element of the fuzzy trace account. (shrink)

According to a regnant criterion of physical equivalence for quantum theories, a quantum field theory (QFT) typically admits continuously many physically inequivalent realizations. This, the second of a two-part introduction to topics in the philosophy of QFT, continues the investigation of this alarming circumstance. It begins with a brief catalog of quantum field theoretic examples of this non-uniqueness, then presents the basics of the algebraic approach to quantum theories, which discloses a structure common even to ‘physically inequivalent’ realizations (...) of a QFT. Finally, it introduces and evaluates a handful of strategies for interpreting quantum theories in the face of the non-uniqueness of their Hilbert space representations. (shrink)

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic nonperturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front (...) Hamiltonian must annihilate the vacuum and have a positive spectrum. We exhibit relations of the Hamiltonian to the nontrivial vacuum structure. (shrink)

Many debates in philosophy focus on whether folk or scientific psychological notions pick out cognitive natural kinds. Examples include memory, emotions and concepts. A potentially interesting type of kind is: kinds of mental representations (as opposed, for example, to kinds of psychological faculties). In this chapter we outline a proposal for a theory of representational kinds in cognitive science. We argue that the explanatory role of representational kinds in scientific theories, in conjunction with a mainstream approach to explanation in (...) cognitive science, suggest that representational kinds are multi-level. This is to say that representational kinds’ properties cluster at different levels of explanation and allow for intra- and inter-level projections. (shrink)

The usual equivalence between the Palalini and metric (or affinity and vielbein) formulations of Einstein theory fails in two spacetime dimensions for its “Kaluza-Klein” reduced (as well as for its standard) version. Among the differences is the necessary vanishing of the cosmological constant in the first-order forms. The purely affine Eddington formulation of Einstein theory also fails here.

In Rules and Representations, first published in 1980, Noam Chomsky lays out many of the concepts that have made his approach to linguistics and human cognition so instrumental to our understanding of language.Chomsky arrives at his well-known position that there is a universal grammar, structured in the human mind and common to all human languages. Based on Chomsky's 1978 Woodbridge Lectures, this edition contains revised versions of the lectures and two new essays.

Arguably the most foundational principle in perception research is that our experience of the world goes beyond the retinal image; we perceive the distal environment itself, not the proximal stimulation it causes. Shape may be the paradigm case of such “unconscious inference”: When a coin is rotated in depth, we infer the circular object it truly is, discarding the perspectival ellipse projected on our eyes. But is this really the fate of such perspectival shapes? Or does a tilted coin retain (...) an elliptical appearance even when we know it’s circular? This question has generated heated debate from Locke and Hume to the present; but whereas extant arguments rely primarily on introspection, this problem is also open to empirical test. If tilted coins bear a representational similarity to elliptical objects, then a circular coin should, when rotated, impair search for a distal ellipse. Here, nine experiments demonstrate that this is so, suggesting that perspectival shapes persist in the mind far longer than traditionally assumed. Subjects saw search arrays of three-dimensional “coins,” and simply had to locate a distally elliptical coin. Surprisingly, rotated circular coins slowed search for elliptical targets, even when subjects clearly knew the rotated coins were circular. This pattern arose with static and dynamic cues, couldn’t be explained by strategic responding or unfamiliarity, generalized across shape classes, and occurred even with sustained viewing. Finally, these effects extended beyond artificial displays to real-world objects viewed in naturalistic, full-cue conditions. We conclude that objects have a remarkably persistent dual character: their objective shape “out there,” and their perspectival shape “from here.”. (shrink)

To understand Self-Representationalism you need to understand its family. Self-Representationalism is a branch of the Meta-Representationalist family, and according to theories in this family what distinguishes conscious mental representations from unconscious mental representations is that conscious ones are themselves the target of a mental meta¬-representational state. A mental state M1 is thus phenomenally conscious in virtue of being suitably represented by some mental state M2. What distinguishes the Self-Representationalist branch of the family is the claim that M1 and (...) M2 must be the same token mental state, so a mental state is phenomenally conscious in virtue of suitably representing itself. This Self-Representationalist branch of the family divides into further branches, giving us specific implementations of the Self-Representationalist approach. But before asking whether we should adopt Self-Representationalism, and in what form, we should reflect on why Meta-Representationalism is an attractive family in the first place. After all, Self-Representationalist theories trade on their family name, claiming to deliver on the promises that drive the Meta-Representationalist approach. The two most important promises of Meta-Representationalism are: a) the promise of capturing the transitivity of consciousness and; b) the promise of rendering consciousness naturalisable. I discuss each in turn. (shrink)

Under representation -- The aesthetic regime of representation -- The pathological sublime: pleasure and pain in the racial regime -- Race under representation -- Representation's coup -- The aesthetic taboo: aura, magic, and the primitive.