The aim of this paper is modest. It is argued that if the nature of the "equivalence" between first-quantized particle theories and second-quantized (Fock Space) theories is examined closely, if the inadequacies of de Muynck's "indexed particle" version of Fock Space are recognized, and if the question is not begged against modal metaphysics, then van Fraassen's attempted deflation of ontological issues in quantum theory can be seen to fail.

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We (...) build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics. (shrink)

We present a solution to the ghost problem in fourth order derivative theories. In particular we study the Pais–Uhlenbeck fourth order oscillator model, a model which serves as a prototype for theories which are based on second plus fourth order derivative actions. Via a Dirac constraint method quantization we construct the appropriate quantum-mechanical Hamiltonian and Hilbert space for the system. We find that while the second-quantized Fock space of the general Pais–Uhlenbeck model does indeed contain the negative (...) norm energy eigenstates which are characteristic of higher derivative theories, in the limit in which we switch off the second order action, such ghost states are found to move off shell, with the spectrum of asymptotic in and out S-matrix states of the pure fourth order theory which results being found to be completely devoid of states with either negative energy or negative norm. We confirm these results by quantizing the Pais–Uhlenbeck theory via path integration and by constructing the associated first-quantized wave mechanics, and show that the disappearance of the would-be ghosts from the energy eigenspectrum in the pure fourth order limit is required by a hidden symmetry that the pure fourth order theory is unexpectedly found to possess. The occurrence of on-shell ghosts is thus seen not to be a shortcoming of pure fourth order theories per se, but rather to be one which only arises when fourth and second order theories are coupled to each other. (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)

Some arguments, based on the possible spontaneous violation of the cosmological principle (represented by the observed large-scale structures of galaxies), on the Cartan geometry of simple spinors, and on the Fock formulation of hydrogen atom wave equation in momentum space, are presented in favor of the hypothesis that space-time and momentum space should be both conformally compactified and should both originate from the two four-dimensional homogeneous spaces of the conformai group, both isomorphic (S 3 ×S 1)/Z (...) 2 and correlated by conformal inversion, but should not necessarily be identified with them. Within this framework, the possible common origin for the SO(4) symmetry underlying the geometrical structure of the Universe, of Kepler orbits, and of the H atom is discussed. One of the consequences of the proposed hypothesis could be that any quantum field theory should be naturally free from both infrared and ultraviolet divergences. But then physical spaces defined as those where physical phenomena may be best described through some set of fields, could be different from those homogeneous spaces. A simple, exactly soluble, toy model, valid for a two-dimensional spacetime, is presented where the conjectured conformally compactified homogeneous spaces are both isomorphic to (S 1 ×S 1)/Z 2,while the possible physical spaces could be two finite lattices which are dual since Fourier transforms, represented by finite, discrete, sums, may be well defined on them. (shrink)

Following a bi-cylindrical model of geometrical dynamics, our study shows that a 6D-gravitational equation leads to geodesic description in an extended symmetrical time–space, which fits Hubble-like expansion on a microscopic scale. As a duality, the geodesic solution is mathematically equivalent to the basic Klein–Gordon–Fock equations of free massive elementary particles, in particular, the squared Dirac equations of leptons. The quantum indeterminism is proved to have originated from space–time curvatures. Interpretation of some important issues of quantum mechanical reality (...) is carried out in comparison with the 5D space–time–matter theory. A solution of lepton mass hierarchy is proposed by extending to higher dimensional curvatures of time-like hyper-spherical surfaces than one of the cylindrical dynamical geometry. In a result, the reasonable charged lepton mass ratios have been calculated, which would be tested experimentally. (shrink)

We analyze different aspects of our quantum modeling approach of human concepts and, more specifically, focus on the quantum effects of contextuality, interference, entanglement, and emergence, illustrating how each of them makes its appearance in specific situations of the dynamics of human concepts and their combinations. We point out the relation of our approach, which is based on an ontology of a concept as an entity in a state changing under influence of a context, with the main traditional concept theories, (...) that is, prototype theory, exemplar theory, and theory theory. We ponder about the question why quantum theory performs so well in its modeling of human concepts, and we shed light on this question by analyzing the role of complex amplitudes, showing how they allow to describe interference in the statistics of measurement outcomes, while in the traditional theories statistics of outcomes originates in classical probability weights, without the possibility of interference. The relevance of complex numbers, the appearance of entanglement, and the role of Fock space in explaining contextual emergence, all as unique features of the quantum modeling, are explicitly revealed in this article by analyzing human concepts and their dynamics. (shrink)

We extend the work of French and Redhead [1988] further examining the relation of quantum statistics to the assumption that quantum entities have the sort of identity generally assumed for physical objects, more specifically an identity which makes them susceptible to being thought of as conceptually individuatable and labelable even though they cannot be experimentally distinguished. We also further examine the relation of such hypothesized identity of quantum entities to the Principle of the Identity of Indiscernibles. We conclude that although (...) such an assumption of identity is consistent with the facts of quantum statistics, methodological considerations show that we should take quantum entities to be entirely unindividuatable, in the way suggested by a Fock space description. (shrink)

We extend the work of French and Redhead [1988] further examining the relation of quantum statistics to the assumption that quantum entities have the sort of identity generally assumed for physical objects, more specifically an identity which makes them susceptible to being thought of as conceptually individuatable and labelable even though they cannot be experimentally distinguished. We also further examine the relation of such hypothesized identity of quantum entities to the Principle of the Identity of Indiscernibles. We conclude that although (...) such an assumption of identity is consistent with the facts of quantum statistics, methodological considerations show that we should take quantum entities to be entirely unindividuatable, in the way suggested by a Fock space description. (shrink)

We support the authors' claims, except that we point out that also quantum structure different from quantum probability abundantly plays a role in human cognition. We put forward several elements to illustrate our point, mentioning entanglement, contextuality, interference, and emergence as effects, and states, observables, complex numbers, and Fock space as specific mathematical structures.

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)

The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle ℋ over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of ℋ is a resolution kernel Hilbert space (...) ℋ $_{\bar \eta }^{(\rho )} $ constructed in terms of generalized coherent states $\bar \eta $ ρ related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter ρ. The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from ℋ $_{\bar \eta }^{(\rho )} $. (shrink)

We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to quantum field theory. By means of the Dirac sea model—exemplified in the electron sector of the standard model neglecting radiation—we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the level of wave (...) functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem, and explains the appearance of creation and annihilation events. 1Bohmian Mechanics from Quantum Mechanics to Quantum Field Theory2The Dirac Sea Model3Equilibrium States and the Vacuum4Excitations of the Vacuum and the Fock Space Formalism5The Appearance of Particle Creations and Annihilations6The Merits of the Bohmian Approach. (shrink)

This is a volume containing papers honoring Patrick Suppes (1922-2014). All contributors have worked directly with Suppes or/and with his ideas. The book also contains one of the last papers by Suppes (co-authored by two of his collaborators). -/- The work of Suppes touches many different areas, ranging from meteorology to physics, through logic, mathematics, psychology, neuroscience, education, painting, but he was first of all and above all a philosopher, always questioning, but not in vain. There are not many philosophers (...) who can be proud of having written influential math textbooks, contributed decisively to the philosophical foundations of science, helped to develop research in real labs, promoted new forms o education (computer-assisted learning and the EGPY – Education Program for Gifted Youth). -/- Since the range of interest of Suppes was very broad, so is the variety of topics dealt with in this volume. The work of a researcher is certainly not limited to his own writings, but also has to be appreciated through the work of the people he has been working with and influenced. From this point of view the work of Suppes is very impressive, and the present book contributes to show that. -/- This is a follow up of a special issue of the journal Synthese, New Directions in the Foundations of Science, edited by Béziau and Krause, after a meeting they organized with Suppes in Florianópolis (Brazil) in 2002 for his 80th birthday. -/- Jean-Yves Béziau worked with Suppes at Stanford University for two years (2000 and 2001) and has been continuously working in the Suppes tradition of logic, methodology and philosophy of science, which emphasizes structures and models. -/- Décio Krause has used Suppes’ approach to the axiomatization of scientific theories in many fields. With J.C.M. Magalhães, he presented a ``Suppes predicate” for genetics and natural selection and with S. French he developed a Suppes predicate for quantum field theories via Fock spaces. (shrink)

The practice of describing multiparticle quantum systems in terms of labeled particles indicates that we think of quantum entities as individuatable. The labels, together with particle indistinguishability, create the need for symmetrization or antisymmetrization (or, in principle, higher-order symmetries), which in turn results in “surplus formal structure” in the formalism, formal structure which corresponds to nothing in the real world. We argue that these facts show quanta to be unindividuatable entities, things in principle incapable of supporting labels, and so things (...) which support no factual difference_if two of them are thought of as being switched. When thinking of the metaphysics of quanta, we should eschew the misleading labels of the tensor product Hilbert space formalism and prefer the ontologically more faithful description of the Fock space formalism. This conception eliminates puzzles about the quantum statistics of bosons. (shrink)

Scattering states in quantum electrodynamics can not be represented in Fock space (i.e., as states with finitely many incoming and outgoing free photons), since most collisions involve the emission of infinitely many soft photons. At present, there exist two alternative proposals for an appropriately modified structure of the asymptotic state space of quantum electrodynamics. According to the “infraparticle” proposal, each charged particle would be accompanied by an appropriate cloud of infinitely many soft photons, whereas according to the (...) “infravacuum” proposal these clouds would be replaced by a common soft photon background. The second (less popular) idea is illustrated and motivated here by simple model calculations. (shrink)

This paper studies the model of the quantum electrodynamics (QED) of a single nonrelativistic electron due to W. Pauli and M. Fierz and studied further by P. Blanchard. This model exhibits infrared divergence in a very simple context. The infrared divergence is associated with the inequivalence of the Hilbert spaces associated with the free Hamiltonian and with the complete Hamiltonian. Infrared divergences that are visible in the perturbative description disappear in the space of the clothed electrons. In this model (...) when the Hamiltonian is expressed in terms of the “physical” fields that create the electron together with its cloud of soft photons, the variational principle suggested earlier can be applied. At finite time the Heisenberg field of the model acts in the space of the perturbative electron together with a finite number of perturbative photons, while the “physical” field can be chosen to act in the space of the exact (“physical”) electron eigenstates together with a finite number of physical photons. The space of the physical (or clothed) electron states can be chosen to be a Fock space. (shrink)

We derive an expression for the relation between two scattering transition amplitudes which, reflect the same dynamics, but which differ in the description of their initial and final state vectors. In one version, the incident and scattered states are elements of a perturbative Fock space, and solve the eigenvalue problem for the “free” pari of the Hamiltonian—the part that remains after the interactions between particle excitations have been “switched off”. Alternatively, the incident and scattered states may be coherent (...) state that are transforms of these Fock states. In earlier work, we reported on the scattering amplitudes for QED, in which a unitary transformation relates perturbative and nonperturbative sets of incident and scattered states. In this work, we generalize this earlier result to the case of transformations that are not necessarily unitary and that may not have unique inverses. We discuss the implication of this relationship for Abelian and non-Abelian gauge theories in which the “transformed”, nonperturbative states implement constraints, such as Gauss’s law. (shrink)

Huggett and Weingard's critical review provides an opportunity to continue the interpretive examination of quantum field theory in terms of some specific issues as well as comparison of alternative approaches to the subject. This note recasts their example of inequivalent Fock spaces in an effort to further clarify what it illustrates. Questions are addressed about the role of analogy in developing quantum field theory and about the conflict between formal vs. concrete methods in both physics and its interpretation, continuing (...) the well-known historical debate between Pierre Duhem and Clark Maxwell. Huggett and Weingard's examination very usefully occasions clarification on some points of exposition which, it is hoped, will make An Interpretive Introduction to Quantum Field Theory a more useful resource for understanding this subject. (shrink)

This paper outlines a framework that may provide a mathematically rigorous quantum field theory. The framework relies upon the methods of nonstandard analysis. A theory of nonstandard inner product spaces and operators on these spaces is first developed. This theory is then applied to construct nonstandard Fock spaces which extend the standard Fock spaces. Then a rigorous framework for the field operators of quantum field theory is presented. The results are illustrated for the case of Klein-Gordon fields.

We analyze the correspondence between a five-dimensional U(1)gauge invariant theory and four-dimensional scalar QED, where the fifth dimension (τ)is an invariant parameter of evolution of the manifestly covariant one-particle sector as well as for the full Fock space. The correspondence is represented by the limit in which the width of the photon mass distribution Δs tends to zero and large τ correlations occur. In the limiting procedure, calculation of a twopoint diagram shows that the PauliVillars regularization is intrinsically (...) related to these longrange correlations. (shrink)

Being formalized inside the S-matrix scheme, the zigzagging causility model of EPR correlations has full Lorentz and CPT invariance. EPR correlations, proper or reversed, and Wheeler's smoky dragon metaphor are respectively pictured in spacetime or in the momentum-energy space, as V-shaped, A-shaped, or C-shaped ABC zigzags, with a summation at B over virtual states |B〉 〈B|. An exact “correspondence” exists between the Born-Jordan-Dirac “wavelike” algebra of transition amplitudes and the 1774 Laplace algebra of conditional probabilities, where the intermediate summations (...) |B) (B| were over “real hidden states.” While the latter used conditional (or transition) probabilities (A|C) = (C|A), the former uses transition (or conditional) amplitudes 〈A|C〉 = 〈C|A〉*. The formal parrallelism breaks down at the level of interpretation because (A|C) = |〈A|C〉|2. CPT invariance implies the Fock and Watanabe principle that, in quantum mechanics, retarded (advanced) waves are used for prediction (retrodiction), an expression of which is 〈Ψ| U |Φ〉 = 〈Ψ| UΦ〉 = 〈ΦU|Φ〉, with |Φ〉 denoting a preparation, |Ψ〉 a measurement, and U the evolution operator. The transformation |Ψ〉 = |UΦ〉 or |Φ〉 = |U−1Ψ〉 exchanges the “preparation representation” and the “measurement representation” of a system and is ancillary in the formalization of the quantum chance game by the “wavelike algebra” of conditional amplitude. In 1935 EPR overlooked that a conditional amplitude 〈A|C〉 = Σ 〈A|B〉〈B|C〉 between the two distant measurements is at stake, and that only measurements actually performed do make sense. The reversibility 〈A|C〉 = 〈C|A〉* implies that causality is CPT-invariant, or arrowless, at the microlevel. Arrowed causality is a macroscopic emergence, corollary to wave retardation and probability increase. Factlike irreversibility states repression, not suppression, of “blind statistical retrodiction”—that is, of “final cause.”. (shrink)

At the heart of chemistry lies the periodic system of chemical elements. Despite being the cornerstone of modern chemistry, the overall structure of the periodic system has never been fully understood from an atomic physics point of view. Group-theoretical models have been proposed instead, but they suffer from several limitations. Among others, the identification of the correct symmetry group and its decomposition into subgroups has remained a problem to this day. In an effort to deepen our limited understanding of the (...) periodic law, we have extended the traditional Lie algebraic framework to account for the peculiar degeneracy structure of the periodic system. Starting from the four-dimensional hidden symmetry and accidental degeneracy of the hydrogen atom, as first revealed by Fock in 1935, our research has mainly focussed on the way this SO(4) symmetry of the Coulomb potential gets broken in the periodic system as a consequence of the transformation of the hydrogenic (n, l) filling order to the Madelung (n+l, n) order due to electronic repulsions, relativistic effects and spin-orbit couplings. In this PhD dissertation, a new left-step format of the periodic table is first proposed on the basis of the Madelung rule. Following the particle physics tradition, the chemical elements are then considered as various states of some 'atomic matter', which is described by a non-compact spectrum-generating dynamical Lie group. The chemical elements are shown to form a basis for a single infinite-dimensional degeneracy space of the SO(4,2) ⊗ SU(2) group. An explanation for the period doubling is then proposed in terms of a particular symmetry breaking of the SO(4,2) group to the anti de Sitter SO(3,2) group. The Madelung rule is rationalised on the basis of nonlinear Lie algebras which reflect the screening of the Coulomb hole. This opens new perspectives for a symmetry-based understanding of how the periodic law emerges from its quantum mechanical foundations, and holds the future promise of complementing our current phenomenological approach by a direct atomic physics approach. (shrink)

The characteristic features of ortho- and para-helium are investigated within the framework of Relativistic Schrödinger Theory (RST). The emphasis lies on the conceptual level, where the geometric and physical properties of both RST field configurations are inspected in detail. From the geometric point of view, the striking feature consists in the splitting of the $\mathfrak{u}(2)$ -valued bundle connection $\mathcal{A}_{\mu}$ into an abelian electromagnetic part (organizing the electromagnetic interactions between the two electrons) and an exchange part, which is responsible for their (...) exchange interactions. The electromagnetic interactions are mediated by the usual four-potentials A μ and thus are essentially the same for both types of field configurations, where naturally the electrostatic forces (described by the time component A 0 of A μ) dominate their magnetostatic counterparts (described by the space part A of A μ). Quite analogously to this, the exchange forces are as well described in terms of a certain vector potential (B μ), again along the gauge principles of minimal coupling, so that also the exchange forces split up into an “electric” type ( $\rightsquigarrow B_{0}$ ) and a “magnetic” type ( $\rightsquigarrow {\bf B}$ ). The physical difference of ortho- and para-helium is now that the first (ortho-) type is governed mainly by the “electric” kind of exchange forces and therefore is subject to a stronger influence of the exchange phenomenon; whereas the second (para-) type has vanishing “electric” exchange potential (B 0 ≡ 0) and therefore realizes exclusively the “magnetic” kind of interactions ( $\rightsquigarrow {\bf B}$ ), which, however, in general are smaller than their “electric” counterparts. The corresponding ortho/para splitting of the helium energy levels is inspected merely in the lowest order of approximation, where it coincides with the Hartree–Fock (HF) approximation. Thus RST may be conceived as a relativistic generalization of the HF approach where the fluid-dynamic character of RST implies many similarities with the density functional theory. (shrink)

The idea that the mass m of an elementary particle is explained in the semi-classical approximation by quantum-mechanical zero-point vacuum fluctuations has been applied previously to spin-1/2 fermions to yield a real and positive constant value for m, expressed through the spinorial connection Γ i in the curved-space Dirac equation for the wave function ψ due to Fock. This conjecture is extended here to bosonic particles of spin 0 and spin 1, starting from the basic assumption that all (...) fundamental fields must be conformally invariant. As a result, in curved space-time there is an effective scalar mass-squared term $m_{0}^{2}=-R/6=2\varLambda_{\mathrm{b}}/3$ , where R is the Ricci scalar and Λ b is the cosmological constant, corresponding to the bosonic zero-point energy-density, which is positive, implying a real and positive constant value for m 0, through the positive-energy theorem. The Maxwell Lagrangian density $\mathcal{L} =- \sqrt{-g}F_{ij}F^{ij}/4$ for the Abelian vector field F ij ≡A j,i −A i,j is conformally invariant without modification, however, and the equation of motion for the four-vector potential A i contains no mass-like term in curved space. Therefore, according to our hypothesis, the free photon field A i must be massless, in agreement with both terrestrial experiment and the notion of gauge invariance. (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)

Given the preponderance of corporate social responsibility initiatives across the corporate landscape and the correspondingly escalating demand for volunteers who participate in these initiatives, a need exists to better understand how to effectively motivate their voluntary engagement with tasks. Against this backdrop, this study argues the need to enhance their volunteer work meanings. We hypothesize that pride in volunteer work and volunteering as a calling are determinants of perceptions of the meaningfulness of volunteer work. In addition, we reveal that an (...) organization’s social responsibility climate (SRC) is a key moderator in these relationships. Interestingly, an SRC is a double-edged sword such that it strengthens the relationship between meaning and pride, yet weakens the relationship between meaning and calling. Findings are discussed, along with managerial implications and future research directions. (shrink)

According to representionalists, qualia-the introspectible properties of sensory experience-are exhausted by the representational contents of experience. Representationalists typically advocate an informational psychosemantics whereby a brain state represents one of its causal antecedents in evolutionarily determined optimal circumstances. I argue that such a psychosemantics may not apply to certain aspects of our experience, namely, our experience of space in vision, hearing, and touch. I offer that these cases can be handled by supplementing informational psychosemantics with a procedural psychosemantics whereby a (...) representation is about its effects instead of its causes. I discuss conceptual and empirical points that favor a procedural representationalism for our experience of space. (shrink)