Showing papers on "Scalar field published in 1969"
TL;DR: In this paper, the formalism of nonlinear realizations is used to treat the spontaneous violation of conformal symmetry, and the associated "Goldstone" particles, characterized by a four-vector and a scalar field, are unusual in that they possess mass.
Abstract: Use is made of the formalism of nonlinear realizations to treat the spontaneous violation of conformal symmetry. The associated "Goldstone" particles, which are characterized by a four-vector and a scalar field, are unusual in that they possess mass.
140 citations
TL;DR: The main existence and uniqueness theorem of Part 1 is applied to three specific problems, namely, (a) the symmetric, dual, nonlinear programs of Dantzig, Eisenberg, and Cottle, (b) the saddle point problem of a differentiable scalar function over an unbounded product set, and (c) the equilibrium-point problem of ann-person game as mentioned in this paper.
Abstract: The main existence and uniqueness theorem of Part 1 is applied to three specific problems, namely, (a) the symmetric, dual, nonlinear programs of Dantzig, Eisenberg, and Cottle, (b) the saddle point problem of a differentiable scalar function over an unbounded product set, and (c) the equilibrium point problem of ann-person game.
98 citations
TL;DR: In this article, a vector theory based on the equatious equation is used to derive linear homogeneous fourth-order equations satisfied by the longitudinal electric and magnetic field components for a medium in which the permittivity decreases monotonically from the propagation axis.
Abstract: This work is a theoretical study of waves in a circular-cylindrical radially inhomogeneous guiding medium. A vector theory based upon Maxwell's equatious is used to derive linear homogeneous fourth-order equations satisfied by the longitudinal electric and magnetic field components for a medium in which the permittivity decreases monotonically from the propagation axis. The percentage change of permittivity from the guide axis to some radius a is assumed small. For modes with propagation constants approximately equal to the wave number at guide center, all field components are shown to satisfy second-order differential equations. In particular, all transverse field components are proportional to a single scalar function. In a Iossless system with no containing boundary, a new class of polynomial-Gaussian solutions describes the longitudinal fields for the case of a quadratically decreasing permittivity, while the transverse fields are Gaussian-Laguerre. Mode patterns, propagation constants, and orthogonality relations are given. It is shown analytically that the modes tend to TE or TM as the mode order increases. Moreover, the transverse fields become dominant at large wave numbers, and the fields become tightly bound to the guide axis as the wave number and/or inhomogeneity increases. Studies of more general permittivity variations and wall effects will be reported shortly.
82 citations
01 Jan 1969
TL;DR: The validity of Huygens' principle in the sense of Hadamard's "minor premise" for scalar wave equations on curved space-time was investigated in this article.
Abstract: The validity of Huygens' principle in the sense of Hadamard's ‘minor premise’ is investigated for scalar wave equations on curved space-time. A new necessary condition for its validity in empty space-time is derived from Hadamard's necessary and sufficient condition using a covariant Taylor expansion in normal coordinates. A two component spinor calculus is then employed to show that this necessary condition implies that the plane wave space-times and Minkowski space are the only empty space-times on which the scalar wave equation satisfies Huygens' principle.
76 citations
TL;DR: In this article, the authors give a general theory of renormalization and an intrinsic characterization for renormalized products; their existence in finite-dimensional situations; and a specialization to a certain quantum process underlying all free Bose-Einstein quantum fields.
60 citations
TL;DR: Theoretical and experimental aspects of the diffraction of gaussian laser beams by the straight edge bounding an opaque plane are investigated in this article, based upon the Kirchhoff scalar wave theory in the Fresnel limit.
Abstract: Theoretical and experimental aspects of the diffraction of gaussian laser beams by the straight edge bounding an opaque plane are investigated. Theoretical analysis is based upon the Kirchhoff scalar wave theory in the Fresnel limit, assuming an incident electromagnetic field having spatial amplitude and phase variation appropriate to a fundamental-mode gaussian beam. Experimental observation consisting of irradiance as a function of position is in good agreement with this theory. Both theoretical and experimental results are found to depend strongly on gaussian-beam parameters.
58 citations
TL;DR: In this article, the Einstein field equations are solved for the metric representing static coupled gravitational and zero-rest-mass scalar fields that depend on at most two variables, and several metrics are then analyzed to determine what changes occur in their singular structure when a zerorest mass scalar field is coupled to a vacuum gravitational field.
Abstract: The Einstein field equations are solved for the metric representing static coupled gravitational and zero-rest-mass scalar fields that depend on at most two variables Several metrics are then analysed to determine what changes occur in their singular structure when a zero-rest-mass scalar field is coupled to a vacuum gravitational field In certain cases it is found that the addition of a zero-rest-mass scalar field can have the effect of changing some of the topological properties of the singularities of the corresponding vacuum field
29 citations
TL;DR: In this article, the response of pi electrons in large organic molecule to scalar field for coronene, showing oscillator strength enhancement near single particle excitation band, was investigated.
Abstract: Response of pi electrons in large organic molecule to scalar field for coronene, showing oscillator strength enhancement near single particle excitation band
25 citations
TL;DR: In this article, the Brans-Dicke gravitational scalar field is geometrized in the spirit of the Rainich-Misner-Wheeler geometrization of electromagnetism and an explicit expression for this field in terms of geometrical quantities is given.
Abstract: The Brans‐Dicke gravitational scalar field is geometrized in the spirit of the Rainich‐Misner‐Wheeler geometrization of electromagnetism. Geometric equations are derived which imply that the Brans‐Dicke field is present and an explicit expression is given for this field in terms of geometrical quantities.
14 citations
TL;DR: In this article, the generalized LSZ asymptotic condition gives the free LSZ fields with discrete and continuous mass spectrum, and the reduction formulae, defining generalized scattering amplitudes, are introduced.
Abstract: We consider the scalar field operator φ(x; s) describing by means of its one-particle states thes-wave stable bound states andS-wave two-particle states. The complete formulation of local quantum field theory for such field operator is presented. The generalized LSZ asymptotic condition gives the free asymptotic fields with discrete and continuous mass spectrum. The reduction formulae, defining generalized scattering amplitudes, are introduced. The unitarity condition and the notion of unstable free particle are discussed. The physical interpretation of the generalized scattering amplitudes is given.
13 citations
TL;DR: In this article, two types of variational principles, each of them equivalent to the linear mixed problem for parabolic equations with initial and combined boundary conditions, are discussed, and a variational characterization of the original problem, expressed in terms of a scalar function (temperature) is presented.
Abstract: New types of variational principles, each of them equivalent to the linear mixed problem for parabolic equation with initial and combined boundary conditions having been suggested by physicists, are discussed. Though the approach used here is purely mathematical so that it makes possible application to all mixed problems of mathematical physics with parabolic equations, only the example of heat conductions is used to show the physical interpretation. The principles under consideration are of two kinds. The first kind presents a variational characterization of the original problem, expressed in terms of a scalar function (temperature). The principles of the second kind characterize the same problem, formulated in terms of other variables, e.g. of a vector function (heat flux or entropy displacements).
TL;DR: In this paper, a matrix formalism is developed for calculating the elastically scattered waves diffracted by an infinite plane parallel crystal, which makes it possible to cover both Laue and Bragg reflected waves under the same formalism.
Abstract: A matrix formalism is developed for calculating the elastically scattered waves diffracted by an infinite plane parallel crystal. Introduction of projection operators makes it possible to cover both Laue and Bragg reflected waves under the same formalism.
TL;DR: In this article, the Schrodinger approach to wave mechanics is applied to free fields instead of particles, and the operators are constructed from the fields as the coordinates and functional derivatives with respect to these fields as momenta, which thus obey the canonical commutation relations.
Abstract: We present a detailed discussion of the Schrodinger approach to wave mechanics applied to free fields instead of particles. The state vector is a functional of the fields and a function of time, and the operators are constructed from the fields as the co-ordinates and functional derivatives with respect to these fields as the momenta, which thus obey the canonical commutation relations. We first study the complex scalar field along the lines of the harmonic oscillator in ordinary quantum mechanics, and we indicate briefly what changes are introduced when the field is real. Next we discuss the massive Lorentz vector field, examining the usual difficulties related to the scalar part, such as negative energies and the indefinite metric. We proceed to discuss the electromagnetic field, with special attention given to the constraints of the theory; we do this both in the usual manner where the potentials are the generalized co-ordinates and in a variation where the fields themselves are the co-ordinates. In both ways we obtain a gauge-independent theory with no redundant variables and no indefinite metric in the space of state vectors. We also discuss the spinor field briefly, but we soon realize that this method is not applicable in its present form. We do not obtain this way any new results, but we explore a new method that brings fresh insights to the problems that beset the quantum theory of fields.
TL;DR: In this article, it is shown that every Poincare and TCP invariant symmetry of the theory, implemented unitarily, which mapps localized elements of the field algebra into operators almost local with respect to the former (such a symmetry we call a physical one) can be defined uniquely in terms of the incoming or outgoing fields and ann-dimensional (real) orthogonal matrix.
Abstract: Let us consider a theory ofn scalar, real, local, Poincare covariant quantum fields forming an irreducible set and giving rise to one particle states belonging to the same mass different from zero. The vacuum is unique. It is shown under fairly weak assumptions that every Poincare and TCP invariant symmetry of the theory, implemented unitarily, which mapps localized elements of the field algebra into operators almost local with respect to the former (such a symmetry we call a physical one) can be defined uniquely in terms of the incoming or outgoing fields and ann-dimensional (real) orthogonal matrix. The symmetry commutes with the scattering matrix. Incidentally we show also that the symmetry groups are compact. A special case of these symmetries are the internal symmetries and symmetries induced by locally conserved currents local with respect to the basic fields and transforming under the same representation of the Poincare group. We may make linear combinations out the original fields resulting in complex fields and its complex conjugate in a suitable way. The inspection of the representations of the groupsSO(n) and their subgroups sheds some light on the s.c. generalized Carruthers Theorem concerning the self- and pair-conjugate multiplets.
TL;DR: The principal component of the parabolic-reflector focal-plane electric field distribution is derived from scalar wave theory in a form providing a simple analytic representation of the field in terms of available tabulated functions not restricted to large focal-length/diameter ratios.
Abstract: The principal component of the parabolic-reflector focal-plane electric-field distribution is derived from scalar wave theory in a form providing a simple analytic representation of the field in terms of available tabulated functions not restricted to large focal-length/diameter ratios.
Journal Article•
TL;DR: In this paper, a new formulation of the scalar field equation or the KleinGordon equation in the presence of external tensor vector Ai(x) and scalar c(x)-field is given.
Abstract: A new formulation of the scalar field equation or the KleinGordon equation in the presence of external tensor vector Ai(x) and scalar c(x) field is given, which is covariant with respect to gauge transformations Ai(x) A;(x) + V iV(X) and conformal transformations of the tensor field gi’(x) exp [0(x)]g\", v(x) and 8(x) are arbitrary functions of x = (xl, x2, ... , x\"). In this case the rest mass square m2(x) defined as the function of given fields rn2 x c 2014 .-20142014-. R 1 V iAi, transforms as follows : m2(x) exp [0(:B’)]~(jc). Here R is the scalar curvature, 17 ;-covariant derivatives in the Riemann space V\" with metric tensor the reciprocal of A~ = It is shown that in considering the class of the scalar wave equations with a constant mass one deals with the metrics gij(x) = which depend implicitly on given tensor, vector and scalar fields. For a potential vector field ~iAj = ~jAi one has the wave equation obtained earlier in ref. [1] which describes the free motion [2] in the Riemann space Vn and possesses correct group properties (contrary to the equation + ~~ = 0 considered usually in extension of the relativistic quantum mechanics and quantum field theory for the case of space-time with nonvanishing curvature). As an example, the scalar field geometrization problem is considered for the relativistic spinless particle wave equation.
TL;DR: In this paper, a cosmic field is introduced that produces a negative pressure, following the work of Pachner, in order to obtain models of the homogeneous Isotropic universe that can oscillate without going through a singular state.
Abstract: In order to obtain models of the homogeneous Isotropic universe that can oscillate without going through a singular state, a cosmic field is introduced that produces a negative pressure, following the work of Pachner. One is led to single out a particular form for this field. If one adds to the Einstein field equations an expression corresponding to this field, taking into account the existence of a cosmic time, one obtains theC-field of Hoyle and Narlikar for the case of conservation of matter.
TL;DR: In this article, the maximum number of scalar functions of wavevector needed to represent the general cumulant of order n of isotropic turbulence is determined, and it is shown that N(4) = 4, N(5) = 6, and N(6) = 9.
Abstract: The maximum number N(n) of scalar functions of wavevector needed to represent the general cumulant of order n of isotropic turbulence is determined. In addition to reproducing the known results that N(2) = 1, N(3) = 2, it is shown that N(4) = 4, N(5) = 4, N(6) = 9, etc.
TL;DR: In this paper, the cone bands theorem is proved for a classical field theory model and a tensor reduction procedure on conserved and asymptotically conserved quantities is defined.
TL;DR: In this article, the divergence of the strangeness conserving vector current to a scalar field was assumed to be proportional to the scalar fields, and Treiman-Goldberger-like relations were obtained with the parameters of the π N scalar-isovector meson.
TL;DR: In this article, the authors considered a quantum theory of one scalar, real, local, Poincare covariant field with the restricted spectrum condition (massive one particle states and a unique vacuum).
Abstract: Let us consider a quantum theory of one scalar, real, local, Poincare covariant fieldA(x) with the restricted spectrum condition (massive one particle states and a unique vacuum). The asymptotic fieldsAin out (x) are assumed to be irreducible. Our conjecture is that under some technical assumptions the “charge” of every real, hermitean, locally conserved, Poincare covariant quantum (pseudo) vector fieldjμ(x) relatively local toA(x), appearing in this theory-vanishes. This means that in a theory of one scalar, real field with a massive particle one can not expect to get symmetry groups induced by conserved (pseudo) vector currents, only by global, selfadjoint, Poincare invariant generators.
TL;DR: In this paper, the Rayleigh-Ritz procedure for functionalities is used to deduce criteria for a nonlinear, relativistic, theory of two coupled self-interacting quantum fields to admit physically realistic vacuum, one-quantum, and twoquantum stationary states.
Abstract: The Rayleigh-Ritz procedure for functionalities is used to deduce criteria for a nonlinear, relativistic, theory of two coupled self-interacting quantum fields to admit physically realistic vacuum, one-quantum, and two-quantum stationary states These criteria suggest that for two-quantum bound and scattering states to be admitted, mass renormalization, together with renormalization of the generic interaction coefficients is required The form of the renormalization is derived and discussed
TL;DR: In this article, the authors compared the radiated energy momentum of a massive classical scalar field from a point source in the mass zero limit with the radiation emitted in a mass zero theory and found that the total radiated number diverges like log m−1 owing to contributions from particles with energies O(m0) but with ultrarelativistic speeds.
TL;DR: In this article, the authors investigated the nature of fluid flow when a spheroid is suspended in an infinitely extending elastico-viscous fluid defined by the constitutive equations given byOldroyd orRivlin andEricksen, and is made to perform small amplitude oscillations along its axis.
Abstract: The present paper investigates the nature of the fluid flow when a spheroid is suspended in an infinitely extending elastico-viscous fluid defined by the constitutive equations given byOldroyd orRivlin andEricksen, and is made to perform small amplitude oscillations along its axis. The solution of the vector wave equation is expressed in terms of the solution of the corresponding scalar wave equation, without the use ofHeine's function or spheroidal wave functions. Two special cases (i) a sphere and (ii) a spheroid of small ellipticity, are studied in detail.
TL;DR: In this article, a proper-time method is applied to a scalar field in interaction with a weak gravitational field, and the coordinate arbitrariness of the linearized gravitational theory is treated as the counterpart of electromagnetic gauge.
TL;DR: In this article, the authors obtained the transfer equation for the scattering of electromagnetic waves in a system comprising a large number of statistically independent particles spherical in shape under the condition cσκ−1 ≪ 1∶ c is the density of the number of particles, σ the scattering cross section for a single particle, and κ the wave number.
Abstract: Using the iteration method, the author obtains the transfer equation for the scattering of electromagnetic waves in a system comprising a large number of statistically independent particles spherical in shape under the condition cσκ−1 ≪ 1∶ c is the density of the number of particles, σ the scattering cross section for a single particle, and κ the wave number. The method is easily extended to the scattering of scalar waves.
TL;DR: In this paper, it was shown that any general covariant field theory may be described in terms of scalar fields, i.e. that the set of all general covariants is equivalent to its subset of scalars.
Abstract: A theorem of Aczel and Golab is strengthened and simplified. According to the new theorem any local geometric object psi A(x) may be expressed as a differential concomitant of a suitable set of local scalars SB(x). As a consequence, it is proved that any generally covariant field theory may be described in terms of scalar fields, i.e. that the set of all general covariant field theories is equivalent to its subset of scalar field theories.