Showing papers on "Scalar field published in 1980"
545 citations
379 citations
TL;DR: In this article, a generalization of the Haag-Kastler axioms for local observables to Lorentzian manifolds is proposed, which is intended to resolve ambiguities in the construction of quantum field theories on manifolds.
Abstract: We propose a generalization of the Haag-Kastler axioms for local observables to Lorentzian manifolds. The framework is intended to resolve ambiguities in the construction of quantum field theories on manifolds. As an example we study linear scalar fields for globally hyperbolic manifolds.
303 citations
TL;DR: In this paper, the authors show that for the case of a Klein-Gordon scalar field propagating in an arbitrary static space-time, a physically sensible, fully deterministic dynamical evolution prescription can be given.
Abstract: Ordinary Cauchy evolution determines a solution of a partial differential equation only within the domain of dependence of the initial data surface. Hence, in a nonglobally hyperbolic space‐time, one does not have fully deterministic dynamics. We show here that for the case of a Klein–Gordon scalar field propagating in an arbitrary static space‐time, a physically sensible, fully deterministic dynamical evolution prescription can be given. If the cosmic censor hypothesis should be overthrown, a prescription of this sort could rescue deterministic physics.
287 citations
TL;DR: In this article, it was shown that scalar and possibly other supersymmetric theories are characterized by the existence of a transformation of the Bose fields with the property that the image of the full bosonic action is the free action and the Jacobi-determinant of the transformation equals the Matthews-Salam-Seiler determinant.
212 citations
TL;DR: The role played by boundary contributions to the integrated quantum mechanical propogator for a finite system is emphasised in this paper, where the local stress tensor is calculated for a scalar field at finite temperature in a static spacetime with boundaries.
209 citations
TL;DR: In this article, the authors apply adiabatic regularisation to a scalar field propagating in a Robertson-Walker universe with arbitrary coupling to the scalar curvature.
Abstract: Adiabatic regularisation is applied to a scalar field propagating in a Robertson-Walker universe with arbitrary coupling to the scalar curvature. Explicit expressions for the expectation value of the quantum stress tensor in an adiabatic vacuum are obtained. This calculation yields the terms which are to be subtracted from the divergent mode-sum expressions for expectation values of the stress tensor to give a finite, renormalised stress tensor. It is shown that the removal of the infinite terms in this subtraction procedure corresponds to the renormalisation of coupling constants in Einstein's equation. A short description is given of the way in which adiabatic regularisation produces a trace anomaly.
177 citations
TL;DR: In this paper, the Riemann curvature tensor tensor R/sub abgd/ is renormalized by renormalization group equations in Minkowskimore space-time and the Lagrange function couple f/sup 2/ to the curvature scalar R with a coupling constant h.
162 citations
TL;DR: In this article, the MGST(6/80) model was used to derive a thirteenth degree and order spherical harmonic geomagnetic field model, which utilized both scalar and high-accuracy vector data and fit that data with root-mean-square deviations of 8.2, 6.9, 7.6 and 7.4 nT.
Abstract: Magsat data from the magnetically quiet days of November 5-6, 1979, were used to derive a thirteenth degree and order spherical harmonic geomagnetic field model, MGST(6/80). The model utilized both scalar and high-accuracy vector data and fit that data with root-mean-square deviations of 8.2, 6.9, 7.6 and 7.4 nT for the scalar magnitude, B(r), B(theta), and B(phi), respectively. The model includes the three first-order coefficients of the external field. Comparison with averaged Dst indicates that zero Dst corresponds with 25 nT of horizontal field from external sources. When compared with earlier models, the earth's dipole moment continues to decrease at a rate of about 26 nT/yr. Evaluation of earlier models with Magsat data shows that the scalar field at the Magsat epoch is best predicted by the POGO(2/72) model but that the WC80, AWC/75 and IGS/75 are better for predicting vector fields.
145 citations
TL;DR: In this paper, the spectrum of the free scalar field in rotating coordinates is calculated for an orbiting observer using these coordinates, and the peak energy appears to be dependent only on the torsion of the observer's world line.
Abstract: Second quantization of the free scalar field is carried out in rotating coordinates and the spectrum of vacuum fluctuations is calculated for an orbiting observer using these coordinates. Normal-mode decomposition is identical to that in Minkowski coordinates except for the definition of positive-frequency modes. Unlike the uniformly accelerating observer, the orbiting observer predicts that the Minkowski vacuum will contain no particles as he would define them. The spectrum of vacuum fluctuations is composed of the usual zero-point energy plus a contribution arising from the observer's acceleration. The latter is not, as with uniformly accelerated motion, thermal. The peak energy appears to be dependent only on the torsion of the observer's world line.
130 citations
TL;DR: In this article, a scalar-field theory with a lambdaphi/sup 4/ self-interaction is studied in space-times with a non-Minkowskian topology.
Abstract: Scalar-field theory with a lambdaphi/sup 4/ self-interaction is studied in space-times with a non-Minkowskian topology. An application of the effective potential to symmetry breaking is discussed. In addition, expressions for the vacuum energy density and topological mass to order lambda are obtained for a theory which is massless at the tree-graph level. One of the cases which is considered is the scalar-field version of the Casimir effect. In this case we also obtain the one-loop vacuum energy density for the massive scalar field and discuss its renormalization.
TL;DR: In this article, the authors studied scalar field theories for which the interaction term of the Hamiltonian is cubic in the fields, and the renormalization group functions for these models were presented up to and including, three-loop contributions, giving critical exponents to order epsilon 3 in 6-epsilon dimensions.
Abstract: The authors study scalar field theories for which the interaction term of the Hamiltonian is cubic in the fields. They indicate the circumstances for which field theory models of this type represent continuous phase transitions. The renormalisation group functions for these models are presented up to, and including, three-loop contributions, giving critical exponents to order epsilon 3 in 6- epsilon dimensions. The exponent sigma which characterises the Yang-Lee edge singularity is given explicitly to this order.
TL;DR: In this article, a technique for reducing the problem of the ultraviolet divergences and their removal to a free field problem is developed, which is an example of a problem to which a rather general method can be applied.
Abstract: We develop a technique for reducing the problem of the ultraviolet divergences and their removal to a free field problem. This work is an example of a problem to which a rather general method can be applied. It can be thought as an attempt towards a rigorous version (in 2 or 3 space-time dimensions) of the analysis of the structure of the functional integrals developed in [9], the underlying mechanism being essentially the same as in [11,3].
TL;DR: In this paper, a class of models which are described by the n → 0 limit of an n-component field theory can be reformulated so as to avoid this limit, and generalisations to a wider class of model classes are discussed.
Book•
01 Jan 1980
TL;DR: In this article, a mathematical theory of bifurcation in mathematics and applications is presented, with a focus on the stability of stable state solutions of reaction-diffusion Equations.
Abstract: I Bifurcation in mathematics and applications- Mathematical Theory of Bifurcation- Remarks on the Stability of Steady-State Solutions of Reaction-Diffusion Equations- Successive Bifurcations and the Ice-Age Problem- II Bifurcation in Theoretical Physics and Statistical Mechanics Applications- Critical Phenomena in Statistical Mechanics Aspects of Renormalization Group Theory- Lattice Renormalization of Non-Perturbative Quantum Field Theory- The Continuous-Spin, Ising Model of Field Theory and the Renormalization Group- Bifurcations for Maps- Critical Properties of One Dimensional Mappings- Intermittency: A Simple Mechanism of Continuous Transition from Order to Chaos- Metal-Insulator Transition in One-Dimensional Deformable Lattices- Sets of Minimum Capacity, Pade Approximants and the Bubble Problem- Bifurcations in the Diophant Moment Problem- III Yang-Mills Field Theory- Yang-Mills Fields: Semi Classical Aspects- Propagation of the Energy of Yang-Mills Fields- Euclidean Yang-Mills and Related Equations- Existence of Stationary States in Nonlinear Scalar Field Equations- IV Solitons in Physics and in Algebraic Geometry- Solitons: Inverse Scattering Theory and its Applications- New Results on the Nonlinear Boltzmann Equation- Solvable Many-Body Problems and Related Mathematical Findings (and Conjectures)- Riemann Monodromy Problem, Isomonodromy Deformation Equations and Completely Integrable Systems- Pade Approximation and the Riemann Monodromy Problem- V Nonlinear Partial Differential Equations and Applications- Nonlinear Evolution Equations of Schrodinger Type- Asymptotic Behavior of Solutions of Hyperbolic Balance Laws- Nonlinear Problems Arising in the Study of Nematic Liquid Crystals- Some Properties of Functional Invariant Sets for Navier-Stokes Equations- An Introduction to the Time-Dependent Hartree-Fock Theory in Nuclear Physics- List of Participants
TL;DR: In this paper, the analogy between field theory at a finite temperature and field theory in periodically identified flat space-time is discussed and used to deduce the Casimir effect, and the renormalization of a twisted scalar field with a lambdaphi/sup 4/ self-interaction is also discussed.
Abstract: The analogy between field theory at a finite temperature and field theory in periodically identified flat space-time is discussed and used to deduce the Casimir effect. The renormalization of a twisted scalar field with a lambdaphi/sup 4/ self-interaction in periodically identified flat spacetime is also discussed.
TL;DR: In this paper, the authors studied the topological relationship between two scalar fields of a molecular system, the electronic charge density and the Coulombic field generated by the atomic nuclei.
Abstract: This paper is a study of the topological relationship between two scalar fields of a molecular system, the electronic charge density and the Coulombic field generated by the atomic nuclei---the nuclear potential. Because of the essential observation that the only local maxima of ground-state charge distributions occur at the positions of the nuclei, the nuclei are the point attractors of the gradient vector fields derived from the charge density and from the nuclear potential. The basins associated with the set of point attractors in either field partition a molecular system into nucleus-dominated regions. The common boundary of any two such neighboring regions contains a particular critical point which generates a pair of gradient paths linking the neighboring attractors. The union of this pair of gradient paths and their end points is called an interaction line. The network of interaction lines defines an elementary graph of the molecular system which identifies the dominant physical interactions in both the charge density and the nuclear potential. Having defined a unique elementary graph for either scalar field for any molecular geometry, the authors partition the total nuclear-configuration space into a finite number of regions. Each region is associated with a particular structure defined as an equivalence class of elementary graphs. The representation of this structural partitioning of nuclear-configuration space is called a structure diagram, which is analogous to a thermodynamic phase diagram. Bader, Nguyen-Dang, and Tal have previously shown that chemical concepts like bonds and molecular structure can be rigorously defined through such a topological analysis of the electronic charge distribution in a molecule. In this paper the authors trace the fundamental role of the nuclear potential in determining the topological properties of this charge distribution. Through a detailed study it is demonstrated that the structure diagrams of the charge density and of the nuclear potential are homeomorphic for the ${\mathrm{H}}_{2}$O system. It is conjectured that this homeomorphism exists in general for any molecular system.
TL;DR: In this article, it was shown that the Born-Infeld scalar field in two-dimensional space-time and the relativistic string in three dimensions are described by the same non-linear Liouville equation.
Abstract: Using the methods of differential geometry it is shown that the Born-Infeld scalar field in two-dimensional space-time and the relativistic string in three dimensions are described by the same non-linear Liouville equation utt-uxx=R eu. This equation admits soliton solutions which may be stable or unstable, and there are periodical solutions among the stable ones. In the quantum case the solitons can be interpreted as massive particles either stable or unstable with respect to the stability of the corresponding classical solution. The periodical soliton generates a series of resonances which have the equidistant mass spectrum. This result appears to be well suited to the theory of the closed relativistic string. In four dimensions the relativistic string is described by the same Liouville equation, but for the complex-valued function u.
TL;DR: In this paper, the second-order self-energy of a nonsimply connected spacetime with topology (S) is calculated and the nonlocal infinities cancel, and it is shown that the theory is renormalizable to this order.
Abstract: A discussion of the renormalization of $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ theory in nonsimply connected spacetime with topology ${S}^{1}\ifmmode\times\else\texttimes\fi{}{R}^{3}$ (periodic in one spatial direction) is given. The presence of either nontrivial topology or local spacetime curvature gives rise to nonlocal divergences which cannot be removed by local counterterms. The second-order self-energy is calculated, and it is shown that the nonlocal infinities cancel so that the theory is renormalizable to this order. This cancellation is shown to occur when the spacetime metric is conformally flat as well as when it is flat. In a nonsimply connected spacetime such as ${S}^{1}\ifmmode\times\else\texttimes\fi{}{R}^{3}$ it is possible to have a new field configuration (the twisted scalar field). It is shown that the second-order self-energy for a twisted, self-interacting scalar field is also free of nonlocal infinities.
TL;DR: It is shown that under very general conditions monochromatic scalar wave fields that have a focus in the sense of geometrical optics possess some simple symmetry properties with respect to the focus.
Abstract: It is shown that under very general conditions monochromatic scalar wave fields that have a focus in the sense of geometrical optics possess some simple symmetry properties with respect to the focus. Certain well-known but poorly understood symmetry properties of the three-dimensional amplitude distribution and phase distribution in the focal region of a uniform converging spherical wave diffracted at a circular aperture are found to be immediate consequences of our results.
TL;DR: In this paper, the authors studied radiative corrections for a scalar field in flat space-time with topology S 1 × R 3, and deduced the critical spatial length below which the symmetry is restored.
TL;DR: In this paper, a systematic discussion of effective field theories, describing a given subset of fields of a quantum field theory, is presented within the context of functional integration, and the results of the complete theory are compared with those of the local, effective theory in a domain where both are supposed to be valid.
Abstract: A systematic discussion of effective field theories, describing a given subset of fields of a quantum field theory, is presented within the context of functional integration. Effective field theories are divided into two classes, natural and unnatural, according to certain independence properties of the counterterms of the theory, defined by minimal subtraction. Natural effective field theories allow independent renormalizations for two distinct mass scales of the theory. A set of constraints, which place restrictions on masses and external momenta, allow the effective field theory to be approximated by a local Lagrangian of dimension four. Predictions of the complete theory are compared with those of the local, effective theory in a domain where both are supposed to be valid. The separate renormalization-group improvement with respect to the two independent mass scales of a natural effective field theory is described. Special problems raised by the presence of massless Goldstone bosons are discussed. The general issues are illustrated by examples from scalar field theories in order to present the discussion simply.
TL;DR: In this paper, a method of optimal truncation (MOOT) was proposed for elastic and acoustic wave scattering, which has tangible and aesthetic advantages over other methods, particularly its convergence properties and its conceptual straightforwardness.
Abstract: Matrix theories of elastic and acoustic wave scattering are reviewed and unified, and a new one is devised and discussed. Called MOOT (method of optimal truncation), it has tangible and aesthetic advantages over other methods, particularly its convergence properties and its conceptual straightforwardness. The exposition is, for simplicity, in terms of scalar waves; the following paper contains detailed applications to scattering of elastic waves. A family of matrix equations, which includes the present method and others, is derived in a simple way from the boundary conditions. Integral equations and their solution by matrix methods are discussed, MOOT is developed and compared with other matrix methods, symmetry principles are developed and their enforcement discussed, and certain computational methods, details, and limitations are expounded. Briefly, we proceed by expanding the scattered wave in a truncated series of eigenfunctions of the unperturbed wave equation, and determine the expansion coefficient...
01 Jan 1980
TL;DR: In this paper, the existence of a ground state and infinitely many bound states is proved under assumptions which are "nearly optimal" using a variational technique, and some results on bifurcation from the essential spectrum are derived for this class of problems.
Abstract: We report on some recent results concerning existence of solutions for nonlinear scalar field equations that lead to semilinear elliptic boundary value problems in ℝN. Such problems arise in a wide variety of contexts in physics (solitons in nonlinear Klein-Gordon or Schrodinger equations, euclidean scalar fields, statistical mechanics, cosmology, nonlinear optics etc…). Existence of a ground state and of infinitely many bound states is proved under assumptions which are “nearly optimal”, using a variational technique. Other methods of resolution are also presented. Some results on bifurcation from the essential spectrum are derived for this class of problems. A generalization of the existence results for systems of equations is also provided here. Lastly, in the appendix, we present some numerical computations emphasizing some qualitative properties of these equations.
01 Jan 1980
TL;DR: In this article, a generalized Stochastic Differential Calculus in homogenization is proposed, which is a generalised version of the Calculus of Differential Equations.
Abstract: Causal Analysis in Terms of White Noise.- to Stochastic Differential Calculus.- A Generalized Stochastic Calculus in Homogenization.- Interaction Picture for Stochastic Differential Equations.- Path Integrals, Stationary Phase Approximations and Complex Histories.- Stochastic Dynamics and the Semiclassical Limit of Quantum Mechanics.- Asymptotic Expansion of Fresnel Integrals Relative to a Non-Singular Quadratic Form.- Scaling Limits of Generalized Random Processes.- Renormalization Group Analysis of Some Higly Bifurcated Families.- Anticommutative Integration and Fermi Fields.- Homogeneous Self-Dual Cones and Jordan Algebras.- Generators of One-Parameter Groups of *-Automorphisms on UHF-Algebras.- Automorphisms of Certain Simple C*-algebras.- Non-Commutative Group Duality and the Kubo-Martin-Schwinger Condition.- A Uniqueness Theorem for Central Extensions of Discrete Products of Cyclic Groups.- to W*-Categories.- Net Cohomology and Its Application to Field Theory.- Construction of Specifications.- On the Global Markov Property.- Uniqueness and Global Markov Property for Euclidean Fields and Lattice Systems.- Martingale Convergence and the Exponential Interaction in IR.- On Dia- and Paramagrietic Properties of Yang-Mills Potentials.- A New Look at Generalized, Non-Linear ?-Models and Yang-Mills Theory.- 1/N Expansions and the O(N) Nonlinear ?-Model in Two Dimensions.- On the z2 Lattice Higgs System.- Fluctuation of the Interface of the Two-Dimensional Ising Model.- The Stability Problem in ?4 Scalar Field Theories.- Summary.
CERN1
TL;DR: In this article, an exact expression for the Green function of the covariant Laplace operator was derived for self-dual monopoles with arbitrary positions using the ADHM formalism developed for instantons.
TL;DR: In this paper, a simple, efficient finite element method has been presented for the solution of a variety of scalar field problems in two dimensions, based on the mapping of the physical problem domain into an image domain in the w-plane.
Abstract: A simple, efficient finite element method has been presented for the solution of a variety of scalar field problems in two dimensions. It is based on the mapping of the physical problem domain into an ‘image’ domain in the w-plane. The governing equation(s) and the boundary conditions in the physical plane are also appropriately transformed into the w-plane. The processes of standard finite element analysis are then implemented to obtain a solution in the w-plane.
The method has been explained in detail, with illustrative examples where appropriate; it has several important advantages over the standard finite element method, particularly for the solution of infinite or semi-infinite domain problems. The method has been demonstrated to be simple, efficient, economical and potentially capable of dealing with a large repartoire of two-dimensional problems, including non-homogeneity, nonlinearity, etc.
TL;DR: In this article, an analysis of the evolution of a massive scalar field in a closed mixmaster universe of Bianchi type IX is given, showing that the probability of the model "bouncing" at a very early time is infinitesimally small.
Abstract: An analysis is given of the evolution of a massive scalar field in a closed mixmaster universe of Bianchi type IX. Although the scalar field violates the strong energy condition, the probability of the model ''bouncing'' at a very early time is infinitesimally small; of the order of the ratio of the minimum to maximum sizes of the universe approx. 10/sup -40/.
TL;DR: In this paper, the construction of twisted scalar and spinor field configurations in Minkowski spacetime is described, and the vacuum expectation value of the energy-momentum tensor of such a quantized twisted field is calculated for the case of both scalar strings and spinors.
Abstract: The construction of twisted scalar and spinor field configurations in Minkowski spacetime is described. Twisted field configurations are normally associated with a nonsimply connected space; however, it is shown that it is also possible to construct such configurations in a simply connected space. For each choice of a line in three-dimensional space there exists an inequivalent twisted scalar and spinor field configuration, referred to as strings. The vacuum expectation value of the energy-momentum tensor of such a quantized twisted field is calculated for the case of both scalar strings and spinor strings. It is found to be singular along the chosen line. The energy density off of this line is positive for scalar strings and negative for spinor strings. However, it is shown that the total energy of both types of strings is zero. Nonrelativistic quantum mechanics of these twisted field configurations is discussed, and the eigenfunctions and energy levels of a twisted particle in a Coulomb field are calculated.