Field Theory Physics Research Articles

REFLECTIONS ON THE SPATIOTEMPORAL ASPECTS OF THE QUANTUM WORLD

The proper resolution of the so-called measurement problem requires a "top-down" conception of the quantum world that is opposed to the usual "bottom-up" conception, which builds on an intrinsically and maximally differentiated manifold. The key to that problem is that the fuzziness of a variable can manifest itself only to the extent that less fuzzy variables exist. Inasmuch as there is nothing less fuzzy than the metric, this argues against a quantum-gravity phenomenology and suggests that a quantum theory of gravity is something of a contradiction in terms — a theory that would make it possible to investigate the physics on scales that do not exist, or to study the physical consequences of a fuzziness that has no physical consequences, other than providing a natural cutoff for the quantum field theories of particle physics.

An elastoplastic theory of dislocations as a physical field theory with torsion

We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastic material as a T(3) gauge theory. We obtain Yang-Mills-type field equations which express the force and the moment equilibrium. Additionally, we discuss several constitutive laws between the dislocation density and the moment stress. For a straight screw dislocation, we find the stress field which is modified near the dislocation core due to the appearance of moment stress. For the first time, we calculate the localized moment stress, the Nye tensor, the elastoplastic energy and the modified Peach-Koehler force of a screw dislocation in this framework. Moreover, we discuss the straightforward analogy between a screw dislocation and a magnetic vortex. The dislocation theory in solids is also considered as a three-dimensional effective theory of gravity.

Two-time physics in field theory

A field theory formulation of two-time physics in d+2 dimensions is obtained from the covariant quantization of the constraint system associated with the OSp(n|2) worldline gauge symmetries of two-time physics. Interactions among fields can then be included consistently with the underlying gauge symmetries. Through this process a relation between Dirac's work in 1936 on conformal symmetry in field theory and the more recent worldline formulation of two-time physics is established while providing a worldline gauge symmetry basis for the field equations in d+2 dimensions. It is shown that the field theory formalism goes well beyond Dirac's goal of linearizing conformal symmetry. In accord with recent results in the worldline approach of two-time physics, the d+2 field theory can be brought down to diverse d dimensional field theories by solving the subset of field equations that correspond to the ``kinematic'' constraints. This process embeds the one ``time'' in d-dimensions in different ways inside the d+2 dimensional spacetime. Thus, the two-time d+2 field theory appears as a more fundamental theory from which many one-time d dimensional field theories are derived. It is suggested that the hidden symmetries and relations among computed quantities in certain d-dimensional interacting field theories can be taken as the evidence for the presence of a higher unifying structure in a d+2 dimensional spacetime. These phenomena have similarities with ideas such as dualities, AdS-CFT correspondence and holography.

The physical projector and topological quantum field theories:U(1) Chern-Simons theory in 2 + 1 dimensions

The recently proposed physical projector approach to the quantisation of gauge invariant systems is applied to the U(1) Chern-Simons theory in 2+1 dimensions as one of the simplest examples of a topological quantum field theory. The physical projector is explicitely demonstrated to be capable of effecting the required projection from the initially infinite number of degrees of freedom to the finite set of gauge invariant physical states whose properties are determined by the topology of the underlying manifold.

Discussion: Conceptual Foundations of Field Theories in Physics

This discussion provides a brief commentary on each of the papers presented in the symposium on the conceptual foundations of field theories in physics. In Section 2 I suggest an alternative to Paul Teller's (1999) reading of the gauge argument that may help to solve, or dissolve, its puzzling aspects. In Section 3 I contend that Sunny Auyang's (1999) arguments against substantivalism and for “objectivism” in the context of gauge field theories face serious worries. Finally, in Section 4 I claim that Gordon Fleming's (1999) proposal for hyperplane-dependent Newton-Wigner fields differs importantly from his previous arguments about hyperplane-dependent properties in quantum mechanics.

Effective field theory for nuclear physics

I summarize the motivation for the effective field theory approach to nuclear physics, and highlight some of its recent accomplishments. The results are compared with those computed in potential models.

The turn to discourse in social psychology.

Abstract We discuss the emerging turn to discursive social psychology as an alternative to experimental social psychology. We note that the barriers to change are rooted in the history of the discipline, in the failure of researchers to recognize the distinction between movements and actions and in their reluctance to switch from positivist to post-positivist criteria. We outline the tenets of discursive psychology and of its associated method, discourse analysis. Illustrations of discourse analysis are drawn primarily from a recent study of date rape. Throughout, we emphasize the centrality of discourse in social life and the definition of the social being as Homo loquens.Resume Nous discutons du passage a la psychologie sociale discursive comme solution de rechange a la psychologie sociale experimentale. Nous constatons que les obstacles au changement trouvent leur source dans l'histoire de la discipline, dans l'echec des chercheurs a reconnaitre la distinction entre les mouvements et les actions, et dans leur resistance a passer des criteres positivistes aux criteres post-positivistes. Nous soulignons les principes de la psychologie discursive et de l'analyse du discours, methode qui y est associee. Les exemples d'analyse du discours sont principalement tires d'une etude recente sur le viol commis par des connaissances. Dans tout l'article, nous mettons l'accent sur l'importance du discours dans la vie sociale et sur les definitions de l'etre social qu'est l'Homo loquens.A decisive turn in the development of social psychology occurred when social psychology adopted the experimental method under the influence of Kurt Lewin. Lewin (1951) had been inspired by the success of field theory in physics and the possibilities he saw in applying field-theoretic principles of force, tension, constraint and context to the study of social-psychological issues. His experiments in leadership style (autocratic, democratic, laissez-faire) became classics in the new experimental social psychology. Festinger, Lewin's most prominent pupil, along with a phalanx of researchers who subsequently became the standard-bearers of experimental social psychology, adopted Lewin's program, first at MIT and later at Michigan and Minnesota. Festinger took an intuitive and creative insight into social processes (derived from his observation of the circulation of rumours about the consequences of earthquakes in India; Festinger, 1957) into the laboratory to spawn two decades of research on cognitive dissonance. Research on cognitive dissonance became the touchstone of experimental social psychology. Interest in the topic has declined, but the commitment to the experimental method remains seemingly unshaken.This commitment has not gone unchallenged. Experimental social psychology came to experience a crisis of confidence on methodological grounds. The crisis literature focused first on ethical questions (Baumrind, 1964). Should an entire discipline rely on lying (technically, deception) as a necessary methodological tool? This was a difficult question in the politically volatile and optimistic 1960s, and is still so today. It involves more lasting questions concerning, for example, the opacity of results obtained via the strategy of deception (Kroger & Wood, 1980). The crisis literature then turned to methodological concerns. Orne (1962) raised the spectre of demand characteristics: the tendency of social psychological experiments to be peculiar social situations in which subjects respond to the social demands of the experimental situation and not just to the independent variables selected by the experimenter. Control over the subject's responses, the raison d'etre of the experimental method, seemed impaired. Rosenthal (1966) added the notion that in the fragile environment of the social-psychological experiment, the characteristics and expectancies of the experimenter might contribute to the results of the experiment as significantly as the classically defined independent variable. …

Nonlinearity and self-interaction in physical field theories with singularities

We investigate rigorous mathematical modeling of nonlinear problems in physical field theories involving differential geometric objects with singularities. We intend to develop a framework allowing for an unrestricted application of a large class of nonlinear operations to geometric objects, in particular tensor fields representing physical quantities arising in classical electrodynamics and general relativity. A convenient setting for this kind of distributional geometry” is provided by Colombeau's theory of generalized functions (cf. [5]). As a prototype of a genuinely nonlinear problem we work out the details of this approach for a point particle moving in a surrounding field with distributional profile in a simplified model of electromagnetism. A careful analysis of the regularization processes involved indicates how to resolve former inconsistencies.

DEGREES OF FREEDOM AND THE INTERPRETATION OF QUANTUM FIELD THEORY

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

Dislocation theory as a physical field theory

Dislocations are the elementary carriers in many situations of plastic flow. Since they can be seen, counted and typified, e.g. in the electron microscope, and since their presence changes the state of the (elastoplastic) medium, the dislocations have the status of a physical state quantity. In spite of this a continuum theory of elastoplasticity can be built up which does not use the concept of dislocation. However, disregarding the dislocations implies approximation, and this approximation is not always good, in spite of the smallness of the dislocation diameter (order atomic distance). It is discussed how a field theory of dislocations can be developed which takes full account of the dislocational degrees of freedom.

A new construction of lattices from codes over GF(3)

We define a pair of constructions of d-dimensional Z-lattices for d = 0 mod 24 from particular length d ternary linear codes, which supplement the construction of d-dimensional Eisenstein lattices (and hence 2 d-dimensional Z-lattices) given by an extension of the work of Sloane (1979) and Conway and Sloane (1988). We show that these constructions produce all of the Niemeier lattices in the case of self-dual codes of length 24, suggesting, by analogy with previous work concerning binary codes, relevance to the classification problem of self-dual conformal field theories in physics. In addition, our intermediate results are of relevance to the classification of self-dual ternary codes of length 24.

Numerical evaluation of derivatives of the anisotropic piezoelectric Green's functions

One of the most powerful tools in linear physical field theories is the Green's function. For the Green's function method to have any practical significance, G must be evaluated. In addition, the derivatives of G are the quantities one requires to solve a large class of internal stress problems such as dislocations, point force arrays, and inclusions. Numerous schemes have been developed in the past to evaluate G and its derivatives in elastic solids. An extensive review of the subject was given by Bacon, Barnett and Scattergood [1]. In this work we report the development of a simple and accurate computer program for enerating numerical results to the Green's functions and their first and second derivatives r linear piezoelectric materials. The results are evaluated numerically from the integral solutions derived from Fourier transform methods. A Gaussian quadrature program valid for any degree of anisotropy of the medium with a variable number of integration points is developed. The results have been checked with Euler's theorems and with existing analytic solutions in purely elastic and dielectric cases. In illustration we present numerical results for the point defect associated with a dilatation center in gallium arseuide and PZT--6B. Related works of this kind in elasticity can be found in the works by Lie and Koehier [2], Barnett [3J, and Leutz and Bauer [4]. We also mentioned the works of Ghahremani [5] and Gavazzi and Lagoudas [6] who generated numerical results for the Eshelby tensor using Gaussian quadrature formulae. Throughout the text Cartesian tensors will be used and their components will be written by the Judicial notation. Repeated indices indicate summation convention with the index running from 1 to 3.

Association Schemes and Fusion Algebras (An Introduction)

We introduce the concept of fusion algebras at algebraic level, as a purely algebraic concept for the fusion algebras which appear in conformal field theory in mathematical physics. We first discuss the connection between fusion algebras at algebraic level and character algebras, a purely algebraic concept for Bose-Mesner algebras of association schemes. Through this correspondence, we establish the condition when the matrix S of a fusion algebra at algebraic level is unitary or symmetric. We construct integral fusion algebras at algebraic level, from association schemes, in particular from group association schemes, whose matrix S is unitary and symmetric. Finally, we consider whether the modular invariance property is satisfied or not, namely whether there exists a diagonal matrix T satisfying the condition (ST)3 = S 2. We prove that this property does not hold for some integral fusion algebras at algebraic level coming from the group association scheme of certain groups of order 64, and we also prove that the (nonintegral) fusion algebra at algebraic level obtained from the Hamming association scheme H(d, q) has the modular invariance property.

SUPERCONDUCTING AND OTHER PHASES IN QUASI-ONE-DIMENSIONAL CARBON SKELETONS

The condensed phases of poly-Cn group are studied by means of the method of quantum field theory in statistical physics. It follows that the transition temperature for poly-Cn group obeys a power law because of the divergence of the density of states at the Fermi level. This class of materials has the possibility of exhibiting high temperature superconductivity.

STABILITY OF GROUND STATE AND CONDENSED PHASES IN INFINITE POLYACENACENE

The normal ground state stability of infinite polyacenacene is investigated by means of the method of quantum field theory in statistical physics. The condensed phases such as charge density wave (CDW), spin density wave (SDV) and superconducting phases are predicted within the random phase approximation (RPA). In particular, we show that there is a possibility that polyacenacene could be a high temperature superconductor.

Chaos and predicting varix hemorrhage

Despite a wide array of mechanisms implicated in esophagogastric varix hemorrhage, predicting the onset of bleeding or even identifying the dominant factor in its causation has proved elusive. In this article we re-examine variceal pathophysiology and hypothesize that bleeding is rooted in turbulent portal system flow, a phenomenon embodied in the ‘new’ science of chaos and the principles of non-linear, rhythmic fluid dynamics. Analogous to forecasting the weather, predicting turbulent flow hinges on defining the initial physical conditions, and, like the field theory of quantum physics, depends on probabilities and instabilities rather than direct proportional analysis. Based on the complex regional and systemic hemodynamic forces and local physical properties underlying formation and perpetuation of esophagogastric varices, we propose, as with climatologic events, that a relatively minor or remote physiologic adjustment may set into motion a sequence of destabilizing splanchnic blood flow kinetics that ultimately causes a varix to erupt. In other words, the onset of varix bleeding derives from a sudden, erratic switch from disorganized but stable to disruptive turbulent variceal blood flow, and as a ‘chaotic’ phenomenon, is likely to remain for the foreseeable future highly unpredictable.

Jet Extension of Finslerian Gauge Approach

The gauge field figures as a key concept in the modern theory of fundamental physical fields. Various deep and intimate relationships between the gauge field theory proper and the methods of differential geometry of fibered spaces have been recognized for a long time. Usually, such relationships are established in terms of group fibrations such that the fibres are implied to be some of Lie groups (see, e.g., [1–4]). In the present servey-article, which extends basic tools elaborated in the preceding publications [5, 6], the author makes an attempt to reach a higher step of gauge generality by getting over the proper Yang-Mills ansatz that the group character of the fibre must be a steed concept from the very beginning. Instead, it looks quite accessible to begin the gauge analysis with more primary starting point where some appropriate, and motivated in a physical sense, geometrical space is treated as a fibre. Such a generalized program proves to be quite feasible if the notion of diffeomorphisms of fibres in themselves is invoked to serve as the required generalized gauge transformations. Such way of extending the gauge transformation concept seems to be sufficiently natural and fundamental for all.

An extremal criterion for epimorphic regeneration.

Many developing systems obey the principle of continuity: a morphogenetic field, when perturbed, tends to restore the normal local pattern of structures in its organ district. We have investigated physical field theories for a morphogenetic field, seeking constraints which would make a field theory produce the principle of continuity. We assume that during embryonic (ontogenetic) development a leg develops a pattern of positional values and a length which extremize a time-independent functional—the integral, over the length of the leg, of a function of positional values and position. For a single state variable which represents positional value, if a unique extremizing solution for the ontogenetically generated pattern and the length exists, and if no position-dependent functions other than the state variable appear in the integrand, then the principle of continuity is valid: in any regenerated leg the state variable is continuous and each region is locally identical to a region of the ontogenetically generated leg. This proposition is applied to three simple examples. For an exponential gradient and a Jacobi elliptic function there is a set of parameter values and boundary values for which a functional is minimized and the ontogenetically generated leg has an optimal length. Thus a leg which meets these constraints will obey the principle of continuity. However, a functional which when extremized gives a sinusoidal pattern does not in general provide a unique extremal length. Mathematical conditions are discussed under which an ontogenetically generated limb or a regenerated limb represents an asymptotically stable steady state. For a specific model of the transient dynamics in the exponential gradient case, the steady state gradient is asymptotically stable.

Field Theory in Particle Physics, Volume 1 and Quantum Field Theory and Gauge Theories of Strong and Electroweak Interactions

<i>Field Theory in Particle Physics, Volume 1</i> and <i>Quantum Field Theory</i> and <i>Gauge Theories of Strong and Electroweak Interactions</i>

Canonical quantization of a special class of gauge theories

The class of theories (special-class theories) to which the most popular physical field theories belong is described in a general form. Various ways of quantizing special-class theories are considered, and their equivalence is demonstrated. The explicit form of the generators of the gauge transformations are obtained, and the equivalence of the definition of physical functions in the Lagrangian and the Hamiltonian formalisms is demonstrated.