The Hartree–Fock–Popov theory of interacting Bose particles is generalized to the Cooper-pair system with a screened Coulomb repulsive interaction in high-temperature superconductors. At zero temperature, it is found that the condensate density \\) of Cooper pairs is of the order \\simeq 10^{18}\) cm\, consistently with the fact that a small fraction of the total p holes participate in pairing. We find that the phonon velocity c at zero temperature is of the order \\simeq 10\) km s\. The computation (...) shows that the transition temperature \ is a dome-shaped function of the p hole concentration \, which is consistent with experiments. At finite temperature, we find that the condensate fraction \/n\) decreases continuously from \/n\) to zero as the temperature increases from zero to the transition temperature \. For higher temperatures, we find that the repulsive interaction between Cooper pairs drives more Cooper pairs into the condensate. The computation reveals that the phonon velocity c decreases continuously from c to zero as the temperature increases from zero to the transition temperature \. The Cooper-pair system undergoes a first-order phase transition from the normal state to the BEC state. (shrink)

Within the framework of Relativistic Schrödinger Theory (RST), the scalar two-particle systems with electromagnetic interactions are treated on the basis of a non-Abelian gauge group U(2) which is broken down to the Abelian subgroup U(1)×U(1). In order that the RST dynamics be consistent with the (non-Abelian) Maxwell equations, there arises a compatibility condition which yields cross relationships for the links between the field strengths and currents of both particles such that self-interactions are eliminated. In the non-relativistic limit, the RST (...) dynamics becomes identical to the well-known Hartree–Fock equations (for spinless particles). Consequently the original RST field equations may be considered as the relativistic generalization of the Hartree–Fock equations, and the “exchange interactions” of the conventional theory (induced by the anti-symmetrization postulate) do reappear here as ordinary gauge interactions due to a broken symmetry. (shrink)

The relativistic three-particle systems are studied within the framework of Relativistic Schrödinger Theory, with emphasis on the determination of the energy functional for the stationary bound states. The phenomenon of entanglement shows up here in form of the exchange energy which is a significant part of the relativistic field energy. The electromagnetic interactions become unified with the exchange interactions into a relativistic U gauge theory, which has the Hartree–Fock equations as its non-relativistic limit. This yields a general framework (...) for treating entangled states of relativistic many-particle systems, e.g., the N-electron atoms. (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 mean-field theory with the use of the slave-boson functional method has been generalized to take account of the spin- and/or orbital-ordered state in the doubly degenerate Hubbard model. Numerical calculations are presented of the antiferromagnetic orbital-ordered state in the half-filled simple-cubic model. The orbital order in the present theory is much reduced compared with that in the Hartree–Fock approximation because of the large orbital fluctuations. From a comparison of the ground-state energy, the antiferromagnetic orbital state is shown (...) to be unstable against the antiferromagnetic spin state, although the situation becomes reversed when the exchange interaction is negative. (shrink)

Mathematical methods and physical ideas developed by Bogolubov are intensively used in the theory of the atomic nucleus. The variational Hartree-Fock-Bogolubov method and the self-consistent field method found wide application in calculating nuclear spectra and nucleus-nucleus interactions. The development of these methods led to the formulation of the quasiparticle-phonon nuclear model for calculating the properties of nuclear states at low, intermediate, and high excitation energies.

Within quantum chemistry, the electron clouds that surround nuclei in atoms and molecules are sometimes treated as clouds of probability and sometimes as clouds of charge. These two roles, tracing back to Schrödinger and Born, are in tension with one another but are not incompatible. Schrödinger’s idea that the nucleus of an atom is surrounded by a spread-out electron charge density is supported by a variety of evidence from quantum chemistry, including two methods that are used to determine atomic and (...) molecular structure: the Hartree-Fock method and density functional theory. Taking this evidence as a clue to the foundations of quantum physics, Schrödinger’s electron charge density can be incorporated into many different interpretations of quantum mechanics. (shrink)

The problem of responsibility has always been an important factor in moral teachings, for this is a problem not only of theory but of everyday practical life. Any system of moral precepts will be lifeless if it does not postulate some measure of responsibility of an individual for his acts. An unselfish, disinterested life becomes morally damaging if a person cannot foresee the moral consequences of his acts and their effects on the lives of those around him, or if (...) the individual's behavior does not correspond to his convictions and good will but is dictated only by external circumstances. (shrink)

The subject of this study is the special theory of relativity (SRT) by A. Einstein, the debate about which has been going on for more than a hundred years. The aim of the study is to evaluate SRT from the side of whether everything that is discussed in this theory and thus in the new, relativistic physics is possible in nature itself. At the same time, the author pays special attention to three issues: the principle of relativity, the (...) necessary condition for the objectivity of the content of scientific theories and the Einstein style of scientific thinking, which predetermined the ideological component of SRT and all relativistic physics. But such issues as relativistic reductions of lengths and durations, the relativity of simultaneity and a single space-time do not remain without attention. The study revealed the fallacy of a long-standing and widespread opinion about the relativity of properties. The necessary condition for the objectivity of scientific theories is revealed. The natural form of expression of quantities is revealed and the non-relative nature of all natural quantities is shown. The hidden form of relativity inherent in the SRT postulate about the constancy of the speed of light in all inertial reference frames and extended in SRT to the magnitude of all lengths and durations considered in it is revealed. It is shown that such relativity is based on the dependence of the quantities on the choice of their reflection systems. It is shown that such dependence is impossible in nature itself. It is concluded that the SRT is erroneous. At the same time, the factors that served as favorable ground for the emergence and spread of this erroneous theory are listed. (shrink)

The subject of this study is materialism, understood in the broadest sense of this concept: both as a philosophical doctrine and as a way of life corresponding to a certain worldview position. The aim is to clarify the objective role of this worldview position in various fields of human activity. At the center of the research is the question of the essence of materialistic ideas about the world hiding behind the sensually given reality to man. The study consists of two (...) parts, published in separate articles. The first part is devoted to the origins of the materialistic worldview and the main question of philosophy, and in this, its second part, the question of the philosophical problems of non-classical physics is considered, the root of these problems is revealed, a comparative worldview analysis of the basic concepts of classical and non-classical physics is carried out and the overall result of the research is summarized. The methodology of this research is the principle of materialistic monism, according to which absolutely all phenomena of the human-cognizable world can be based only on something material, "influencing". The general conclusions of this study are as follows: the roots of the materialistic worldview go back to the origins of life, to such a condition of successful vital activity of living beings, which is inherently ideological; this condition, called by the author the Main Question of Life, is the historical forerunner of the Main Question of Philosophy; the worldview position, equivalent to the materialistic solution of the OVF, is inherent in the vital activity of absolutely all living beings; all people in their daily and practical activities are born materialists. In addition, this study clarifies the idea of the essence of materialistic teaching; shows the exclusivity of the materialistic worldview as the only true worldview; provides a refined definition of the concept of matter; proves the need to shift the "center of gravity" of modern materialistic teaching from dialectics to the principle of materialistic monism; formulates the missing requirement for scientific theories to ensure their ideological viability; shows the ideological inconsistency the main ideas of the new, non-classical physics. (shrink)

The subject of this study is the problem of the failure of attempts by the scientific community to come to a common understanding of what exactly information can be as something encoded into material structures and moved along with them. At the same time, the following aspects of this problem are considered in detail: what is the immediate cause of the information problem; what are the objective and subjective prerequisites for its appearance; why the unresolved nature of this problem does (...) not interfere with the creation and development of communication systems, control and other "smart" devices; is there any general guideline for finding solutions to such problems, and what is it; what role did the philosophy of information play in turning the problem of information from a private scientific problem into a problem of the ideological level. The main results of the conducted research are as follows: the immediate cause of the information problem has been identified and a comprehensively substantiated solution to this problem has been given; it has been revealed that the incompleteness of the materialistic theory of cognition has become a fertile ground for the appearance of this problem; the circumstances that prevented its completion have been identified; the natural mechanism of control and cognition has been revealed, as a result of which the materialistic theory of cognition has been further developed the source of the ideal in the material world is revealed; it is shown that the mechanistic idea of information coding made the concept of information incompatible with the presence of any objective content; it is revealed what is actually hidden behind the words about information coding and its measurement; the nature of signals and signs is revealed; a kind of bias of the philosophy of information and a general error is revealed all known concepts of information. (shrink)

The relevance of exchange effects for the stability of superheavy nuclei is examined within a linear QHD-II model by comparing Hartree-Fock with meanfield results. To allow a scan of the complete superheavy regime the recently developed local density approximation (LDA) for the exchange potential is employed for the Hartree-Fock level calculations. It turns out that, while many nuclear properties obtained with the LDA approach differ significantly from the corresponding mean-field results, the predictions of the two methods for shell closures are (...) very similar. Furthermore, a comparison with a nonlinear variant of QHD-II shows that many nuclear properties obtained with the LDA in the framework of linear QHD-II are somewhere in-between the corresponding linear and nonlinear mean-field results. This indicates that the LDA exchange partially includes nonlinear contributions, which supports the interpretation of the meson self-coupling as a parametrization of many-body effects. (shrink)

Psychological egoism is the doctrine that all of our actions are ultimately motivated by self-interest, even including seemingly altruistic actions. Although this view is commonly referred to as \vacuous" or \trivially true" because of its immunity to counterexamples, I argue that there are possible observations that can refute this thesis. I describe the experiments, identify the results that could in principle falsify the strongest possible version of psychological egoism and formulate a probabilistic argument against this view. Ultimately, I conclude that (...) a \trivially true" formulation of psychological egoism is an empirical theory that is in all likelihood false. (shrink)

A correct understanding of Hart’s idea of justice and a detailed assessment of the connection between justice and law contributes to a better understanding of his legal-philosophical project. Always consistent with his argument on the separability between law and morality, Hart endorses an account of formal intralegal justice that is intimately connected to law, but not necessarily dependent upon non-legal principles of substantive justice. Hart’s theoretical commitment to a composite concept of formal justice encompasses two elements: first, the imperative to (...) treat like cases alike and different cases differently, and second, the underlying legal criteria that specify the relevant measure of likeness and difference. These elements of Hart’s theory of justice can be traced back to their doctrinal precedents in the texts of Aristotle, Sidgwick, Perelman, Ross, and Del Vecchio. Commentators and critics of Hart’s account of justice seem to agree that this account ought to be expanded by exploring its full effects on the foundations of Hart’s concept of law. When this is achieved, a third element of Hart’s intralegal justice emerges, namely, its rights-allocating function, which is deeply embedded in his account of the rule of recognition, his concept of a legal system, and his idea of law. (shrink)

This paper presents a historical-philosophical reconstruction of Leibniz’s theory of education. In the introduction, I point out the exegetical problems involved in locating Leibniz’s “philosophy of education” within the broader corpus of his works and in uncovering an appropriate theoretical framework within which it is possible to contextualise and reconstruct Leibniz’s thought on education. It is then shown that this framework is provided by Leibniz’s practical philosophy, i.e. his ideas about the optimal state and the common good. I analyse (...) the key theses of Leibniz’s ethics and political philosophy to uncover the background of the idea of the respublica optima and explain how education, in Leibniz’s view, should enable the perfection of the individual and society and contribute to the realisation of the common good. Finally, it is argued that in his educational project Leibniz articulated an idea of the Enlightenment that is far more progressive than the educational ideas of the philosophers we usually associate with the eighteenth-century Enlightenment. (shrink)

The paper adopts an inter-theoretical socio-cultural and -material perspective on the relationship between human + machine learning to propose a new way to investigate the human + machine assistive assemblages emerging in professional work (e.g. medicine, architecture, design and engineering). Its starting point is Hutchins’s (1995a) concept of ‘distributed cognition’ and his argument that his concept of ‘cultural ecosystems’ constitutes a unit of analysis to investigate collective human + machine working and learning (Hutchins, Philos Psychol 27:39–49, 2013). It argues that: (...) (i) the former offers a way to reveal the cultural constitution of and enactment of human + machine cognition and, in the process, the limitations of the computational and connectionist assumptions about learning that underpin, respectively, good old-fashioned AI and deep learning; and (2) the latter offers a way to identify, when amplified with insights from Socio-Materialism and Cultural-Historical Activity Theory, how ML is further rearranging and reorganising the distributed basis of cognition in assistive assemblages. The paper concludes by outlining a set of conjectures researchers that could use to guide their investigations into the ongoing design and deployment of HL + ML assemblages and challenges associated with the interaction between HL + ML. (shrink)

This book proposes a new approach to the question of the juridical domain of natural law with reference to the classical tools of Thomistic formulation. This book adds something new to the intersection between the normative status of natural law and the essence of the juridical domain.

Douglas Hartree and Hilleth Thomas were graduate students together at Cambridge University in the mid-1920s. Each developed an important approximation method to calculate the electronic structure of atoms. Each went on to make significant contributions to numerical analysis and to the development of scientific computing. Their early efforts were fused in the mid-1960s with the development of an approach to the many-particle problem in quantum mechanics called density functional theory. This paper discusses the experiences which led Hartree and Thomas (...) to their approximations, outlines the similarities in their subsequent careers, and highlights the essential role their work played in the foundational papers of modern density functional theory. (shrink)

Modelling reasoning with legal cases has been a central concern of AI and Law since the 1980s. The approach which represents cases as factors and dimensions has been a central part of that work. In this paper I consider how several varieties of the approach can be applied to the interesting case of Popov v Hayashi. After briefly reviewing some of the key landmarks of the approach, the case is represented in terms of factors and dimensions, and further explored using (...) theory construction and argumentation schemes approaches. (shrink)

Berichte zur Wissenschaftsgeschichte, EarlyView.

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.

Vladimir Fock est un scientifique russo-soviétique connu pour diverses contributions à la physique moderne. Il en fut aussi un interprète, développant une position critique face à l’orthodoxie incarnée par Niels Bohr en mécanique quantique et Albert Einstein en relativité générale. Fock ayant adhéré au matérialisme dialectique, l’historiographie sur ses contributions aux débats d’interprétation met généralement l’accent sur sa défense d’une position réaliste, en faveur de l’objectivité du monde extérieur. Le présent article complète cette observation en s’appuyant sur un texte du (...) physicien soviétique jusqu’alors peu connu : « La signification fondamentale des méthodes d’approximation en physique théorique ». En effet, il révèle une forme d’antiréductionnisme essentielle à la compréhension du discours de Fock sur l’interprétation des théories de la physique moderne. (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)

Variable particle masses have sometimes been invoked to explain observed anomalies in low energy nuclear reactions (LENR). Such behavior has never been observed directly, and is not considered possible in theoretical nuclear physics. Nevertheless, there are covariant off-mass-shell theories of relativistic particle dynamics, based on works by Fock, Stueckelberg, Feynman, Greenberger, Horwitz, and others. We review some of these and we also consider virtual particles that arise in conventional Feynman diagrams in relativistic field theories. Effective Lagrangian models incorporating variable mass (...) particle theories might be useful in describing anomalous nuclear reactions by combining mass shifts together with resonant tunneling and other effects. A detailed model for resonant fusion in a deuterium molecule with off-shell deuterons and electrons is presented as an example. Experimental means of observing such off-shell behavior directly, if it exists, is proposed and described. Brief explanations for elemental transmutation and formation of micro-craters are also given, and an alternative mechanism for the mass shift in the Widom–Larsen theory is presented. If variable mass theories were to find experimental support from LENR, then they would undoubtedly have important implications for the foundations of quantum mechanics, and practical applications may arise. (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 describe the picture of physical processes suggested by Edward Nelson’s stochastic mechanics when generalized to quantum field theory regularized on a lattice, after an introductory review of his theory applied to the hydrogen atom. By performing numerical simulations of the relevant stochastic processes, we observe that Nelson’s theory provides a means of generating typical field configurations for any given quantum state. In particular, an intuitive picture is given of the field “beable”—to use a phrase of John (...) Stewart Bell—corresponding to the Fock vacuum, and an explanation is suggested for how particle-like features can be exhibited by excited states. We then argue that the picture looks qualitatively similar when generalized to interacting scalar field theory. Lastly, we compare the Nelsonian framework to various other proposed ontologies for QFT, and remark upon their relative merits in light of the effective field theory paradigm. Links to animations of the corresponding beables are provided throughout. (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)

Previous work has shown that spontaneous collapse of Fock states of identical fermions can be modeled as arising from random Rabi oscillations between two states. In this paper, a mathematical formalism is presented to incorporate this into many-body quantum field theory. This formalism allows for nonlocal collapse in the context of a relativistic system. While there is no absolute time-ordering of events, this approach allows for a coherent narrative of the collapse process.

In the present work we explore the effects that an H impurity produces upon the geometry and electronic structure of the CaTiO 3 crystal considering the cubic and orthorhombic crystallographic lattices of the material. A quantum-chemical method based on the Hartree-Fock formalism and the periodic large-unit-cell model is used throughout the work. The analysis of the results shows that the interstitial H impurity binds to one of the O atoms forming the so-called O-H group. At equilibrium, the O-H distances are (...) found to be equal to 0.89 and 1.04 Å for cubic and orthorhombic lattices respectively. Atomic displacements and relaxation energies are analysed comparing the obtained results in the cubic lattice with those in the orthorhombic lattice. In the cubic phase the computed relaxation energy of vicinity of the O-H group is found to be equal to 1.1 eV and the atomic displacements generally obey the Coulomb law. So, the negatively charged O atoms move outwards from the defective region by about 0.09 Å while the positively charged Ti and Ca atoms move towards the defective region by about 0.05 and 0.01 Å respectively. A similar effect is observed in the orthorhombic lattice of CaTiO 3 doped with an H atom. It is necessary to mention that different O positions in the orthorhombic structure are considered for the O-H bond creation. The computed relaxation energies of the atomic displacements in this structure are found to be equal to 2.3 and 2.1 eV depending on the crystallographic type of the bonding O atom. (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)

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)

The first volume of the Brandeis University Summer Institute lecture series of 1970 on theories of interacting elementary particles, consisting of four sets of lectures. Every summer since 1959 Brandeis University has conducted a lecture series centered on various areas of theoretical physics. The areas are sufficiently broad to interest a large number of physicists and the lecturers are among the original explorers of these areas. The 1970 lectures, presented in two volumes, are on theories of interacting elementary particles. The (...) four lecturers of Volume 1, and the range of the topics they cover, are as follows: Stephen L. Adler on "Perturbation Theory Anomalies": introduction and review of perturbation theory; the VVA triangle anomaly; absence of radiative corrections; generalizations of our results; connection between Ward identity anomalies and commutator anomalies; applications of the Bjorken limit; and breakdown of the Bjorken limit in perturbation theory. Stanley Mandelstam on "Dynamical Applications of the Veneziano formula for the four-point scalar amplitude; factorization; the operator formalism; Veneziano-type quark models; and higher-order Feynman-like diagrams. Steven Weinberg on "Dynamic and Algebraic Symmetries": Introduction; hadron electrodynamics; local symmetries; and chirality. Wolfhart Zimmermann on "Local Operator Products and Renormalization in Quantum Field Theory": introduction; renormalization; operator product expansions; and local field equations. The second volume contains lectures by Rudolf Haag on observables and fields, by Maurice Jacob on duality, by Michael Reed on non-Fock representations, and by Bruno Zumino on effective Lagrangians and broken symmetries. (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 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)

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)

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)

This sixth volume of Collected Papers includes 74 papers comprising 974 pages on (theoretic and applied) neutrosophics, written between 2015-2021 by the author alone or in collaboration with the following 121 co-authors from 19 countries: Mohamed Abdel-Basset, Abdel Nasser H. Zaied, Abduallah Gamal, Amir Abdullah, Firoz Ahmad, Nadeem Ahmad, Ahmad Yusuf Adhami, Ahmed Aboelfetouh, Ahmed Mostafa Khalil, Shariful Alam, W. Alharbi, Ali Hassan, Mumtaz Ali, Amira S. Ashour, Asmaa Atef, Assia Bakali, Ayoub Bahnasse, A. A. Azzam, Willem K.M. Brauers, Bui (...) Cong Cuong, Fausto Cavallaro, Ahmet Çevik, Robby I. Chandra, Kalaivani Chandran, Victor Chang, Chang Su Kim, Jyotir Moy Chatterjee, Victor Christianto, Chunxin Bo, Mihaela Colhon, Shyamal Dalapati, Arindam Dey, Dunqian Cao, Fahad Alsharari, Faruk Karaaslan, Aleksandra Fedajev, Daniela Gîfu, Hina Gulzar, Haitham A. El-Ghareeb, Masooma Raza Hashmi, Hewayda El-Ghawalby, Hoang Viet Long, Le Hoang Son, F. Nirmala Irudayam, Branislav Ivanov, S. Jafari, Jeong Gon Lee, Milena Jevtić, Sudan Jha, Junhui Kim, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Songül Karabatak, Abdullah Kargın, M. Karthika, Ieva Meidute-Kavaliauskiene, Madad Khan, Majid Khan, Manju Khari, Kifayat Ullah, K. Kishore, Kul Hur, Santanu Kumar Patro, Prem Kumar Singh, Raghvendra Kumar, Tapan Kumar Roy, Malayalan Lathamaheswari, Luu Quoc Dat, T. Madhumathi, Tahir Mahmood, Mladjan Maksimovic, Gunasekaran Manogaran, Nivetha Martin, M. Kasi Mayan, Mai Mohamed, Mohamed Talea, Muhammad Akram, Muhammad Gulistan, Raja Muhammad Hashim, Muhammad Riaz, Muhammad Saeed, Rana Muhammad Zulqarnain, Nada A. Nabeeh, Deivanayagampillai Nagarajan, Xenia Negrea, Nguyen Xuan Thao, Jagan M. Obbineni, Angelo de Oliveira, M. Parimala, Gabrijela Popovic, Ishaani Priyadarshini, Yaser Saber, Mehmet Șahin, Said Broumi, A. A. Salama, M. Saleh, Ganeshsree Selvachandran, Dönüș Șengür, Shio Gai Quek, Songtao Shao, Dragiša Stanujkić, Surapati Pramanik, Swathi Sundari Sundaramoorthy, Mirela Teodorescu, Selçuk Topal, Muhammed Turhan, Alptekin Ulutaș, Luige Vlădăreanu, Victor Vlădăreanu, Ştefan Vlăduţescu, Dan Valeriu Voinea, Volkan Duran, Navneet Yadav, Yanhui Guo, Naveed Yaqoob, Yongquan Zhou, Young Bae Jun, Xiaohong Zhang, Xiao Long Xin, Edmundas Kazimieras Zavadskas. (shrink)