Showing papers on "Scalar field published in 1992"

Cosmological 'seed' magnetic field from inflation

Abstract: We extend the canonical exponential potential scalar field inflation modified hot big bang model by adding an inflation epoch coupling, between the scalar field Φ responsible for inflation and an Abelian gauge field A μ , ∞e αΦ F μν F μν (where F μν =∂ μ A ν −∂ ν A μ and α is a parameter)

Nondiffracting X waves-exact solutions to free-space scalar wave equation and their finite aperture realizations

Abstract: The authors report families of generalized nondiffracting solutions of the free-space scalar wave equation, and specifically, a subset of these nondiffracting solutions, which are called X waves. These nondiffracting X waves can be almost exactly realized over a finite depth of field with finite apertures and by either broadband or bandlimited radiators. With a 25-mm diameter planar radiator, a zeroth-order broadband X wave will have about 2.5-mm lateral and 0.17-mm axial -6-dB beam widths with a -6-dB depth of field of about 171 mm. A zeroth-order bandlimited X wave was produced and measured in water by a 10 element, 50-mm diameter, 2.5-MHz PZT ceramic/polymer composite J/sub 0/ Bessel nondiffracting annular array transducer with -6-dB lateral and axial beam widths of about 4.7 mm and 0.65 mm, respectively, over a -6-dB depth of field of about 358 mm. Possible applications of X waves in acoustic imaging and electromagnetic energy transmission are discussed. >

Towards the theory of the electroweak phase transition

Abstract: We investigate various problems related to the theory of the electroweak phase transition. This includes determination of the nature of the phase transition, discussion of the possible role of the higher-order radiative corrections, and the theory of the formation and evolution of bubbles of the new phase. We show, in particular, that no dangerous linear terms in the scalar field $\ensuremath{\varphi}$ appear in the expression for the effective potential. We have found that, for the Higgs-boson mass smaller than the masses of $W$ and $Z$ bosons, the phase transition is of the first order. However, its strength is approximately ⅔ times less than what follows from the one-loop approximation. The phase transition occurs due to production and expansion of critical bubbles. Subcritical bubbles may be important only if the phase transition is very weakly first order. A general analytic expression for the probability of the bubble formation is obtained, which may be used for study of tunneling in a wide class of theories. The bubble-wall velocity depends on many factors, including the ratio of the mean free path of the particles to the thickness of the wall. Thin walls in the electroweak theory have a nonrelativistic velocity, whereas thick walls may be relativistic. A decrease of the cubic term by the factor ⅔ rules out baryogenesis in the minimal version of the electroweak theory. Even though we concentrate in this paper on the phase transition in this theory, most of our results can be applied to more general models as well, where baryogenesis is possible.

Quantum Field Theory of Point Particles and Strings

Abstract: Point Particles * Introduction: Phenomenology Overview * First to Second Quantization * Free Scalar Field Theory * Free Spinor Field Theory * Quantization of the Electromagnetic Field * Self-Interacting Scalar Field Theory * Spinor Quantum Electrodynamics * Functional Calculus * Free Fields in the Schrdinger Representation * Interacting Fields in the Schrdinger Representation * Path Integral Representation of Quantum Mechanics * Path Integrals in Free Field Theory * Interacting Fields and Path Integrals * Yang-Mills and Faddeev-Popov * Hiding the Infinities * Renormalization of QED at 1-Loop * The Effective Action Strings * Basic Ideas and Classical Theory * First Quantization * The Mathematics of Surfaces * Polykovs Integral: The Partition Function for Genus 0 * Higher-Genus Integrals * Scattering Amplitudes * Noncritical Dimensions * Introduction to Superstrings

Branch cuts in the phase function

Abstract: It is shown that, when the scalar field associated with the propagation of a distorted wave function has nulls in its intensity pattern, the phase function that goes with that scalar field has branch points at the location of these nulls and that there are unavoidable 2π discontinuities across the associated branch cuts in the phase function. An analytic proof of this supposition is provided. Sample computer-wave optics propagation results are presented that manifest such unavoidable discontinuities. Among other things, the numerical results are organized in a way that demonstrates that for those cases the branch points are unavoidable. It is found in the sample numerical results that the branch cuts can be positioned so that the 2π discontinuities are located along lines of minimum intensity. This location tends to minimize the physical significance or importance of the discontinuities, a significant consideration for deformable-mirror adaptive optics, for which there is an unavoidable correction error in the vicinity of the branch cut. An algorithm is briefly described that allows the branch cuts to be located automatically and a phase function to be calculated that has discontinuities equal only to 2π discontinuities that are located at the branch cuts.

Probability distribution, conditional dissipation, and transport of passive temperature fluctuations in grid‐generated turbulence

Abstract: The evolution of the scalar probability density function (pdf), the conditional scalar dissipation rate, and other statistics including transport properties are studied for passive temperature fluctuations in decaying grid‐generated turbulence. The effect of filtering and differentiating the time series is also investigated. For a nonzero mean temperature gradient it is shown that the pdf of the temperature fluctuations has pronounced exponential tails for turbulence Reynolds number (Rel) greater than 70 but below this value the pdf is close to Gaussian. The scalar dissipation rate, conditioned on the fluctuations, shows that there is a high expectation of dissipation in the presence of the large, rare fluctuations that produce the exponential tails. Significant positive correlation between the mean square scalar fluctuations and the instantaneous scalar dissipation rate is found when exponential tails occur. The case of temperature fluctuations in the absence of a mean gradient is also studied. Here, the results are less definite because the generation of the fluctuations (by means of fine heated wires) causes an asymmetry in the pdf. The results show, however, that the pdf is close to Gaussian and that the correlation between the mean square temperature fluctuations and the instantaneous scalar dissipation rate is very weak. For the linear profile case, measurements over the range 60≤Rel≤1100 show that the dimensionless heat flux Nu is proportional to Rel0.88 and that the transition from a Gaussian pdf to one with exponential tails occurs at Nu∼31, a value close to transitions observed in other recent mixing experiments conducted in entirely different turbulent flows.

Hierarchal scalar and vector tetrahedra

Abstract: A novel set of scalar and vector tetrahedral finite elements are presented. The elements are hierarchical, allowing mixing of polynomial orders. Scalar orders up to three and vector orders up to two are defined. The vector elements impose tangential continuity on the field but not normal continuity, making them suitable for representing the vector electric or magnetic field. The scalar and vector elements can easily be used in the same mesh, a requirement of many quasi-static formulations. Results are presented for two 50-Hz problems: the Bath cube and the TEAM Workshop problem 7. >

BRST analysis of physical states for 2D gravity coupled to c≤1 matter

Abstract: We consider 2D gravity coupled toc≦1 conformal matter in the conformal gauge. The Liouville system is represented by a free scalar field,φL, with background charge such that the BRST operator imposing reparametrization invariance is nilpotent. We compute the cohomology of this BRST charge on the product of the Fock space ofφL with those of the ghosts and one other free scalar field,φM representing the matter system. From this calculation the physical states of the full theory are determined. For thec<1 case the further projection from the Fock space ofφM to the irreducible representation, using Felder's resolution, reproduces the results of Lian and Zuckerman.

The art of the state

Abstract: Quantum field theory on curved spacetimes lacks an obvious distinguished vacuum state. We review a recent no-go theorem that establishes the impossibility of finding a preferred state in each globally hyperbolic spacetime, subject to certain natural conditions. The result applies in particular to the free scalar field, but the proof is model-independent and therefore of wider applicability. In addition, we critically examine the recently proposed `SJ states', that are determined by the spacetime geometry alone, but which fail to be Hadamard in general. We describe a modified construction that can yield an infinite family of Hadamard states, and also explain recent results that motivate the Hadamard condition without direct reference to ultra-high energies or ultra-short distance structure.

Black holes in higher-derivative gravity theories

Abstract: We study static spherically symmetric solutions of Einstein gravity plus an action polynomial in the Ricci scalar $R$ of arbitrary degree $n$ in an arbitrary dimension $D$. The global properties of all such solutions are derived by studying the phase space of field equations in the equivalent theory of gravity coupled to a scalar field, which is obtained by a field redefinition and conformal transformation. The following uniqueness theorem is obtained: Provided that the coefficient ${a}_{2}$ of the ${R}^{2}$ term in the Lagrangian polynomial is positive then the only static spherically symmetric asymptotically flat solution with a regular horizon in these models is the Schwarzschild solution. Other branches of solutions with regular horizons, which are asymptotically anti-de Sitter, or de Sitter, are also found. An exact Schwarzschild-de Sitter-type solution is found to exist in the $R+a{R}^{2}$ theory if $Dg4$. If terms of cubic or higher order in $R$ are included in the action, then such solutions also exist in four dimensions. The general Schwarzschild-de Sitter-type solution for arbitrary $D$ and $n$ is given. The fact that the Schwarzschild solution in these models does not coincide with the exterior solution of physical bodies such as stars has important physical implications which we discuss. As a byproduct, we classify all static spherically symmetric solutions of $D$-dimensional gravity coupled to a scalar field with a potential consisting of a finite sum of exponential terms.

Cosmic microwave background probes models of inflation.

Abstract: Inflation creates both scalar (density) and tensor (gravity wave) metric perturbations. We find that the tensor-mode contribution to the cosmic microwave background anisotropy on large-angular scales can only exceed that of the scalar mode in models where the spectrum of perturbations deviates significantly from scale invariance. If the tensor mode dominates at large-angular scales, then the value of DeltaT/T predicted on 1 deg is less than if the scalar mode dominates, and, for cold-dark-matter models, bias factors greater than 1 can be made consistent with Cosmic Background Explorer (COBE) DMR results.

Gauge-invariant perturbations in a scalar field dominated universe

Abstract: The authors propose a new covariant and gauge-invariant (GI) treatment of perturbations in a Robertson-Walker universe dominated by a classical scalar field phi . They first set up the formalism, based on the natural slicing of the problem by the surfaces phi =constant, and introduce a set of covariantly defined GI variables. In their approach the whole inhomogeneity of the matter field is incorporated in the GI spatial fluctuations of the momentum psi of phi ; then the GI density perturbations are simply proportional to the momentum perturbations. The inhomogeneity of the geometry is characterized by GI fluctuations of the 3-curvature scalar of the surfaces phi =constant. The time evolution of the matter and curvature perturbations are coupled by a pair of first-order linear differential equations. Correspondingly, each GI variable satisfies a second-order linear homogeneous differential equation. When the background curvature vanishes, k=0, the curvature variable is conserved for perturbation scales larger than the horizon, but this is no longer true in general if k not=0. They discuss simple examples, including the case when more than one scalar field is present, recovering standard results for inflationary universe models. They also demonstrate that in coasting solutions with k=-1, inhomogeneities are damped out on all scales.

The regularized Chapman-Enskog expansion for scalar conservation laws

Abstract: Rosenau has recently proposed a regularized version of the Chapman-Enskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at law wave-numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. The behavior of Rosenau regularization of the Chapman-Enskog expansion (RCE) is studied in the context of scalar conservation laws. It is shown that thie RCE model retains the essential properties of the usual viscosity approximation, e.g., existence of traveling waves, monotonicity, upper-Lipschitz continuity..., and at the same time, it sharpens the standard viscous shock layers. It is proved that the regularized RCE approximation converges to the underlying inviscid entropy solution as its mean-free-path epsilon approaches 0, and the convergence rate is estimated.

On the modeling of scalar diffusion in isotropic turbulence

Abstract: The objectives of the study were to establish the behavior of conditional scalar dissipation and diffusion at the extreme values of mass fraction and to derive and evaluate closure models for these terms using the scalar probability density function. The conditional scalar dissipation, its derivative with respect to mass fraction, and conditional scalar diffusion are all found to be zero at extreme values of mass fraction. A model for conditional scalar dissipation is derived which exhibits the correct behavior at the extreme values of scalar concentration.

Decoherence in quantum electrodynamics and quantum gravity.

Abstract: We treat the interaction of a semiclassical electromagnetic field with a complex scalar field as a continuous measurement process through which certain interference terms between electromagnetic field states may become suppressed---they decohere.'' The formal framework is the functional Schroedinger picture for scalar QED. The reduced density matrix for the electromagnetic field is discussed in detail. We calculate the remaining coherence width for realistic laboratory field strengths. The back reaction of the scalar field on the electromagnetic state is discussed with the help of the Wigner function and is explicitly calculated. We compare our results with the corresponding case in quantum gravity where the radius of the Universe is measured'' by inhomogeneous scalar field modes. We propose to render the decoherence factor finite by summing over a set of rescaled field modes.

A linear eddy sub-grid model for turbulent reacting flows: Application to hydrogen-AIR combustion

Abstract: A new sub-grid mixing model for use in large eddy simulations of turbulent combustion is presented and applied to a hydrogen-air diffusion flame. The sub-grid model is based on Kerstein's Linear Eddy Model (Comb. Sci. Tech 60, 391, 1988), which reduces the description of the scalar field to a locally one-dimensional representation. The formulation involves performing separate linear eddy calculations in each cell to describe the small-scale scalar mixing and reaction process. Convective transport across grid surfaces is accomplished by “splicing” events by which linear eddy elements are copied to and from neighboring grid cells based on the grid-resolved velocity field. The model is first used to predict, the mixing of a conserved scalar in a turbulent shear flow. The model correctly predicts the behavior of the pdf of the scalar field. In particular, it displays a non-marching peak at the preferred mixture fraction as the shear layer is traversed. It is then illustrated how a reduced chemical mechanism can be implemented within the linear eddy subgrid model formulation. The model is used to predict NO formation in a hydrogen-air diffusion flame using a reduced chemical mechanism involving nine reactive scalars.

Vacuum energy in quantum field theory with external potentials concentrated on planes

Abstract: In the presence of an idealized potential on two parallel planes represented by two one-dimensional delta -functions at x3=-d/2 and x3=+d/2 the authors discuss the Feynmann propagators for relativistic scalar and spinor fields. These propagators take into account bound states, scattering states and resonances. The Casimir energy for this configuration is calculated. For massive fields the Casimir force decreases exponentially with rising distances. In the scalar case they find an attractive force and in the spinor case a repulsive force. An attempt to treat the same problem for a massive scalar field using nonrelativistic quantum field theory leads to a vanishing Casimir force.

Mixing characteristics of an inhomogeneous scalar in isotropic and homogeneous sheared turbulence

Abstract: Turbulent mixing of an inhomogeneous passive scalar field is studied in the context of a nonpremixed reacting flow. Direct numerical simulations of an initial steplike scalar field subjected to homogeneous sheared turbulence have been performed and the results compared with those of the case of decaying isotropic turbulence. For both flow conditions, the gradient of the conserved scalar tends to align itself with the axis of the most compressive strain rate and orthogonal to the local vorticity. The magnitude of the scalar gradient is directly influenced by the local strain rate while its orientation is controlled by the local vorticity. Because of the directional features of sheared turbulence, the orientation of the scalar gradient is more ordered than in isotropic turbulence. In addition, the magnitude of vorticity indirectly affects that of the scalar gradient through strain‐rate amplification by vortex stretching. In both flows, regions of high scalar‐gradient magnitude or scalar dissipation (and the...

Computation of 3-D magnetostatic fields using a reduced scalar potential

Abstract: Some improvements to the finite element computation of static magnetic fields in three dimensions using a reduced magnetic scalar potential are presented. Methods are described for obtaining an edge element representation of the rotational part of the magnetic field from a given source current distribution. When the current distribution is not known in advance, a boundary value problem is set up in terms of a current vector potential. An edge element representation of the solution can be directly used in the subsequent magnetostatic calculation. The magnetic field in a DC arc furnace is calculated by first determining the current distribution in terms of a current vector potential. A 3-D problem involving a permanent magnet as well as a coil is solved, and the magnetic field in some points is compared with measurement results. >

Quantum effects near a point mass in (2+1)-dimensional gravity.

Abstract: We investigate the behavior of classical and quantum fields in the conical space-time associated with a point mass in 2 + 1 dimensions. We show that the presence of conical boundary conditions alters the electrostatic field of a point charge leading to the presence of a finite self-force on the charge from the direction of the point mass exactly as if the point mass itself were charged. The conical space-time geometry also affects the zero-point fluctuations of a quantum scalar field leading to the existence of a vacuum polarization $〈{T}_{\ensuremath{\mu}\ensuremath{ u}}〉$ in the (2 + 1)-dimensional analogue of the Schwarzschild metric. The resulting linearized semiclassical Einstein equations ${G}_{\ensuremath{\mu}\ensuremath{ u}}=8\ensuremath{\pi}G〈{T}_{\ensuremath{\mu}\ensuremath{ u}}〉$ possess a well-defined Newtonian limit, in marked contrast to the classical case for which no Newtonian limit is known to exist. An elegant reformulation of our results in terms of the method of images is also presented. Our analysis also covers the nonstatic de Sitter-Schwarzschild metric in 2 + 1 dimensions, in which in addition to the vacuum polarization, a nonzero vacuum flux of energy $〈{T}_{\mathrm{rt}}〉$ is also found to exist. As part of this analysis, we evaluate the scalar field propagator in an $n$-dimensional de Sitter space; as a result some novel features of quantum field theory in odd dimensions are seen to emerge.

Inflation in an exponential-potential scalar field model

Abstract: A spatially flat cosmological scalar field $\ensuremath{\Phi}$ model with the scalar field potential $\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\Phi}}{\sqrt{p}})$, $pg1$, provides a simple class of inflationary cosmologies (which includes the usual exponential expansion inflation) that may be used as an analytical testing ground to help understand the predictions of the inflation model of the very early Universe. We divide the evolution of this model into three distinct epochs: scalar-field dominance and conventional radiation and baryon dominance; in each epoch we only account for irregularities in the dominant form of matter. We present closed-form solutions of the (synchronous gauge) relativistic linear perturbation equations that govern the evolution of inhomogeneities. These classical solutions, augmented with quantum-mechanically motivated initial conditions and joining conditions to match the expressions for the irregularities at the scalar-field-radiation and radiation-baryon transitions, are used to estimate the large-time form of the spectrum of energy-density irregularities, of the local departure velocity from homogeneous expansion, of large-scale fluctuations in the microwave background temperature, and of the gravitational-wave energy density. The inflation epoch results agree with those found from a purely quantum-mechanical analysis. Depending on the value of $p$ this model can have more large-scale power than the usual scale-invariant spectrum (at the expense of less small-scale power) and would seem to be marginally better at forming large-scale structure than the canonical model; however, the decrease in small-scale power serves to exacerbate the problem of late galaxy formation. As the model approaches the exponential expansion inflation limit, the power spectrum tends towards the scale-invariant form, although, in this limit the numerical prefactor diverges. We find that transverse peculiar velocity perturbations are not generated. Normalizing by fitting to the observed large-scale departure velocity, we find that models which stop inflating around ${10}^{7}$-${10}^{16}$ GeV are not obviously observationally inconsistent.

A scalar imaging velocimetry technique for fully resolved four‐dimensional vector velocity field measurements in turbulent flows

Abstract: This paper presents an experimental technique for obtaining fully resolved measurements of the vector velocity field u(x,t) throughout a four‐dimensional spatiotemporal region in a turbulent flow. The method uses fully resolved four‐dimensional scalar field imaging measurements in turbulent flows [Phys. Fluids A 3, 1115 (1991)] to extract the underlying velocity field from the exact conserved scalar transport equation. A procedure for accomplishing this is described, and results from a series of test cases are presented. These involve synthetically generated scalar fields as well as actual measured turbulent flow scalar fields advected numerically by various imposed flow fields. The imposed velocity fields are exactly known, allowing a careful validation of the technique and its potential accuracy. Results obtained from a zeroth iteration of the technique are found to be very close to the exact underlying vector velocity field. Further results show that successive iterations bring the velocity field from the zeroth iteration even closer to the exact result. It is also shown that the comparatively dense velocity field information that this technique provides is well suited for accurate extraction of the more dynamically insightful strain rate and vorticity fields e(x,t) and ω(x,t).

Fluctuations and dissipation for a mirror in vacuum

Abstract: A mirror in vacuum is submitted to a radiation pressure exerted by scattered fields. It is known that the resulting mean force is zero for a motionless mirror, but not for a mirror moving with a non-uniform acceleration. The authors show here that this force results from a motional modification of the field scattering while being associated with the fluctuations of the radiation pressure on a motionless mirror. They consider the case of a scalar field in a two-dimensional spacetime and characterize the scattering upon the mirror by frequency dependent transmissivity and reflectivity functions obeying unitarity, causality and high frequency transparency conditions. They derive causal expressions for dissipation and fluctuations and exhibit their relation for any stationary input. They recover the known damping force at the limit of a perfect mirror in vacuum. Finally, they interpret the force as a mechanical signature of the squeezing effect associated with the mirror's motion.

Stress-energy tensors in anti-de Sitter spacetime.

Abstract: The stress-energy tensors are computed for scalar and spinor fields with arbitrary mass in anti-de Sitter spacetime using the $\ensuremath{\zeta}$-function technique. The results are compared with those obtained by Pauli-Villars regularization. It is found that they agree with one another. The trace anomaly for the Wess-Zumino model (the scalar supermultiplet) in anti-de Sitter spacetime is studied. It is concluded that the trace anomaly must take the "conventional" value in this model although the physical significance of the stress-energy tensor is not clear in anti-de Sitter spacetime. The relation between the $\ensuremath{\zeta}$-function and Pauli-Villars methods in an arbitrary space is also clarified.

Induced QCD at Large N

Abstract: We propose and study at large N a new lattice gauge model , in which the Yang-Mills interaction is induced by the heavy scalar field in adjoint representation. At any dimension of space and any $ N $ the gauge fields can be integrated out yielding an effective field theory for the gauge invariant scalar field, corresponding to eigenvalues of the initial matrix field. This field develops the vacuum average, the fluctuations of which describe the elementary excitations of our gauge theory. At $N= \infty $ we find two phases of the model, with asymptotic freedom corresponding to the strong coupling phase (if there are no phase transitions at some critical $N$). We could not solve the model in this phase, but in the weak coupling phase we have derived exact nonlinear integral equations for the vacuum average and for the scalar excitation spectrum. Presumably the strong coupling equations can be derived by the same method.