Showing papers on "Scalar field published in 1988"
TL;DR: It is argued that a number of models in which the energy density of the scalar field red-shifts in a specific manner are studied could reconcile the low dynamical estimates of the mean mass density with the negligibly small spatial curvature preferred by inflation.
Abstract: The cosmological consequences of a pervasive, rolling, self-interacting, homogeneous scalar field are investigated. A number of models in which the energy density of the scalar field red-shifts in a specific manner are studied. In these models the current epoch is chosen to be scalar-field dominated to agree with dynamical estimates of the density parameter, ${\ensuremath{\Omega}}_{\mathrm{dyn}\mathrm{\ensuremath{\sim}}0.2}$, and zero spatial curvature. The required scalar-field potential is ``nonlinear'' and decreases in magnitude as the value of the scalar field increases. A special solution of the field equations which is an attractive, time-dependent, fixed point is presented. These models are consistent with the classical tests of gravitation theory. The E\"otv\"os-Dicke measurements strongly constrain the coupling of the scalar field to light (nongravitational) fields. Nucleosynthesis proceeds as in the standard hot big-bang model. In linear perturbation theory the behavior of baryonic perturbations, in the baryon-dominated epoch, do not differ significantly from the canonical scenario, while the presence of a substantial amount of homogeneous scalar-field energy density at low red-shifts inhibits the growth of perturbations in the baryonic fluid. The energy density in the scalar field is not appreciably perturbed by nonrelativistic gravitational fields, either in the radiation-dominated, matter-dominated, or scalar-field-dominated epochs. On the basis of this effect, we argue that these models could reconcile the low dynamical estimates of the mean mass density with the negligibly small spatial curvature preferred by inflation.
3,948 citations
TL;DR: In this article, the evolution of scalar fields, of different initial integral length scales, in statistically stationary, homogeneous, isotropic turbulence is studied, and it is shown that the pdf of the scalar tends to a Gaussian self-similar state.
Abstract: The evolution of scalar fields, of different initial integral length scales, in statistically stationary, homogeneous, isotropic turbulence is studied. The initial scalar fields conform, approximately, to ‘‘double‐delta function’’ probability density functions (pdf ’s). The initial scalar‐to‐velocity integral length‐scale ratio is found to influence the rate of the subsequent evolution of the scalar fields, in accord with experimental observations of Warhaft and Lumley [J. Fluid Mech. 88, 659 (1978)]. On the other hand, the pdf of the scalar is found to evolve in a similar fashion for all the scalar fields studied; and, as expected, it tends to a Gaussian. The pdf of the logarithm of the scalar‐dissipation rate reaches an approximately Gaussian self‐similar state. The scalar‐dissipation spectrum function also becomes self‐similar. The evolution of the conditional scalar‐dissipation rate is also studied. The consequences of these results for closure models for the scalar pdf equation are discussed.
553 citations
TL;DR: This paper treats a system of self-interacting bosons described by λφ4 scalar fields in flat space and adopts the closed-time-path (CTP) functional formalism and uses a two-particle irreducible (2PI) representation for the effective action.
Abstract: This is the first of a series of papers which describe the functional-integral approach to the study of the statistical and kinetic properties of nonequilibrium quantum fields in flat and curved spacetimes. In this paper we treat a system of self-interacting bosons described by \ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ scalar fields in flat space. We adopt the closed-time-path (CTP or ``in-in'') functional formalism and use a two-particle irreducible (2PI) representation for the effective action. These formalisms allow for a full account of the dynamics of quantum fields, and put the correlation functions on an equal footing with the mean fields. By assuming a thermal distribution we recover the real-time finite-temperature theory as a special case. By requiring the CTP effective action to be stationary with respect to variations of the correlation functions we obtain an infinite set of coupled equations which is the quantum-field-theoretical generalization of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Truncation of this series leads to dissipative characteristics in the subsystem. In this context we discuss the nature of dissipation in interacting quantum fields.To one-loop order in a perturbative expansion of the CTP effective action, the 2PI formalism yields results equivalent to the leading 1/N expansion for an O(N)-symmetric scalar field. To higher-loop order we introduce a two-time approximation to separate the quantum-field effects of radiative correction and renormalization from the statistical-kinetic effects of collisions and relaxation. In the weak-coupling quasiuniform limit, the system of nonequilibrium quantum fields can subscribe to a kinetic theory description wherein the propagators are represented in terms of relativistic Wigner distribution functions. From a two-loop calculation we derive the Boltzmann equation for the distribution function and the gap equation for the effective mass of the quasiparticles. One can define an entropy function for the quantum gas of quasiparticles which satisfies the H theorem. We also calculate the limits to the validity of the binary collision approximation from a three-loop analysis. The theoretical framework established here can be generalized to nonconstant background fields and for curved spacetimes.
444 citations
01 Jun 1988
TL;DR: This paper presents rendering techniques that use volumes as the basic geometric primitives, and a new method for the visualization of three-dimensional data resulting from numerical simulations and observations of natural phenomena.
Abstract: This paper presents rendering techniques that use volumes as the basic geometric primitives. It defines data structures composed of numerous subvolumes, in excess of 100,000. Over each subvolume, a scalar field describes the variation of some physical quantity. The two rendering methods described herein assume a trilinear variation of this scalar field within each volume element, unlike voxel-based techniques that assume a constant value for each subvolume. The result is a higher order approximation of the structures within the volume. In addition, solid texture mapping, atmospheric attenuation, and transfer functions relating the dynamic range of the scalar field to color and opacity are used to isolate important data features. The result is a new method for the visualization of three-dimensional data resulting from numerical simulations and observations of natural phenomena. This method continuously covers the gap between surface-based and voxel-based techniques.
435 citations
TL;DR: The nonlinear scalar field equation governing the propagation of an unsteadily convected interface is used to derive a convenient expression for the average volume flux through such an interface in a homogeneous flow field, facilitating analysis based on renormalized perturbation theory and numerical simulation.
Abstract: The nonlinear scalar field equation governing the propagation of an unsteadily convected interface is used to derive a convenient expression for the average volume flux through such an interface in a homogeneous flow field. For a particular choice of the initial scalar field, the average volume flux through any such interface is expressed as a volume-averaged functional of the evolving scalar field, facilitating analysis based on renormalized perturbation theory and numerical simulation. It is noted that this process belongs to a different universality class from the propagation model of M. Kardar, G. Parisi, and Y.-C. Zhang (Phys. Rev. Lett. 56, 889 (1986)).
401 citations
TL;DR: In this article, the N-point tree amplitudes of the non-archimedean open string are derived from a simple non-local lagrangian involving a single scalar field (the tachyon) in ambient space-time.
331 citations
TL;DR: In this paper, the authors simulate the transport and mixing of diffusive scalars in turbulent flows using a novel representation of the temporal evolution along a transverse line moving with the mean fluid velocity, where the scalar field along this line evolves by Fickian diffusion, representing molecular processes and by randomly occurring events called block inversions.
Abstract: Transport and mixing of diffusive scalars in turbulent flows are simulated computationally based on a novel representation of the temporal evolution along a transverse line moving with the mean fluid velocity. The scalar field along this line evolves by Fickian diffusion, representing molecular processes, and by randomly occurring events called block inversions. Block inversion, representing the effect of turbulent convection, consists of the random selection of an interval (Y0 − 1/2, Y0 + 1/2) of the line, where the interval size l may he either fixed or randomly selected, and replacement of the scalar field θ(y) within that interval by θ(2y0 For fixed l, the model requires a single input parameter, the Peclet number. To demonstrate the performance of the model, this formulation is used to compute the spatial development of diffusive scalar fields downstream of several source configurations in homogeneous turbulence. Generalization to inhomogeneous turbulence is discussed, as well as a formulati...
320 citations
TL;DR: In this article, the authors consider cosmological models containing a self-interacting scalar field possessing a potential of the form V ( φ ) = Λ exp(− λφ ).
298 citations
TL;DR: In this paper, a second-order closure model for calculating the transport of momentum and passive scalar quantities in turbulent flows is described, which is based on the Reynolds stress and scalar flux balance equations.
Abstract: A second‐order, single‐point closure model for calculating the transport of momentum and passive scalar quantities in turbulent flows is described. Of the unknown terms that appear in the Reynolds stress and scalar flux balance equations, it is those which involve the fluctuating pressure that exert a dominant influence in the majority of turbulent flows. A closure approximation (linear in the Reynolds stress) has been formulated for the velocity‐pressure gradient correlation appearing in the Reynolds stress equation. When this is used in conjunction with previous proposals for the other unknown terms in the stress equation, the proposed model closely simulates most of the data on high Reynolds number homogeneous turbulent flows. For the fluctuating scalar‐pressure gradient correlation appearing in the scalar flux equation, an approximation has been devised that satisfies the linear transformation properties of the exact equation. Additional characteristics of the fluctuating scalar field are obtained from the solution of modeled balance equations for the scalar variance and its ‘‘dissipation’’ rate. The resulting complete scalar field model is capable of reproducing measured data in decaying scalar grid turbulence and strongly sheared, nearly homogeneous flow in the presence of a mean scalar gradient. In addition, applications to the thermal mixing layer developing downstream from a partially heated grid and to a slightly heated plane jet issuing into stagnant surrounds result in calculated profiles in close agreement with those measured.
231 citations
TL;DR: Using the equivalence between the curvature-squared gravity theory and the Einstein theory with a scalar field, it is shown that the potential in the latter system has a very flat plateau.
Abstract: Using the equivalence between the curvature-squared gravity theory and the Einstein theory with a scalar field, we show that the potential in the latter system has a very flat plateau. It turns out that inflation is quite natural but transient in the ${R}^{2}$ cosmology. All anisotropic Bianchi types of space-time except IX approach the de Sitter solution as an attractor, followed by the Friedmann universe after sufficient inflation. We find a similar behavior in higher- (4lDl10) dimensional theories, in which inflation is not exponential-type but power-law-type. The dilaton coupling to the ${R}^{2}$ term is also investigated. The coupling destroys the inflationary solution.
196 citations
TL;DR: In this article, the authors reviewed the evidence for triviality in various field theories and the implications for high energy physics are discussed, and the authors suggested that the presence of fermion fields can rescue a pure φ4 scalar theory from triviality.
TL;DR: The power law inflationary universe model induced by a scalar field with an exponential potential was studied in this paper, where a dissipation term due to particle creation was introduced in the inflation's classical equation of motion.
TL;DR: It is meaningless in minisuperspace of quantum gravity to extend classical paths through this region to a recollapsing phase and higher degrees of freedom are introduced which can produce classical paths by continuous measurement.
Abstract: Wave packets in minisuperspace of quantum gravity are explicitly constructed for a Friedmann model containing either a massless or a massive homogeneous scalar field. Unparametrized tubelike standing waves corresponding to classically returning paths in configuration space can be constructed if a ``final condition'' with respect to the scale factor a is assumed to hold. Sensible wave packets are only obtained for certain discrete values of the mass and only in regions not too close to the classical turning point. Therefore it is meaningless in minisuperspace of quantum gravity to extend classical paths through this region to a recollapsing phase. This suggests that we introduce higher degrees of freedom which can produce classical paths by continuous measurement.
01 Jan 1988
TL;DR: In this paper, it was shown that pure quantum states will appear to decay into mixed states in any theory of quantum gravity that allows the topology of spacetime to be non simply connected.
Abstract: It is shown that pure quantum states will appear to decay into mixed states in any theory of quantum gravity that allows the topology of spacetime to be non simply connected. The reason is that the final state may contain little closed universes. There is no way one can detect the existence of these closed universes, or measure their quantum state. This means that the part of the final state that is in asymptotically flat spacetime, appears to be in a mixed state. The loss of quantum coherence in particle collisions is estimated. It comes from a wormhole connecting two asymptotically euclidean regions. The effect would be significant for scalar particles. It would make any scalar field that was not coupled to a Yang-Mills field constant throughout spacetime. It could have an important effect on Higgs particles but the effect would be small for particles of higher spin.
TL;DR: In this paper, the authors examined the most general theory describing a real scalar field coupled to Einstein gravity in four dimensions and obtained a general non-trivial form of the Bianchi identities for this theory.
Abstract: The author examines the most general theory describing a real scalar field coupled to Einstein gravity in four dimensions. The author shows that the stress tensor of the scalar field always has the structure of a fluid stress tensor. In the case that the scalar field is minimally coupled to gravity, this reduces to a perfect-fluid structure. In addition, the author obtains a generally non-trivial form of the Bianchi identities for this theory, investigates the kinematics of the scalar field and shows how to extend the analysis to include complex scalars and scalar multiplets. Finally, the author discusses the ground-state solutions of the theory, with special attention given to the case when the scalar field potential is polynomial in the fields. The author shows that the gravity-scalar coupling has interesting consequences for the spontaneous breakdown of gauge symmetries and for the observable value of the cosmological constant.
TL;DR: Using the effective scalar field theory of the p-adic string, it is shown the equivalence of two previously derived sets of classical Feynman rules: one by the present authors, the other by Brekke et al.
Abstract: Using the effective scalar field theory of the $p$-adic string, we show the equivalence of two previously derived sets of classical Feynman rules: one by the present authors, the other by Brekke et al. We use this equivalence to demonstrate a symmetry of the $p$-adic tree amplitude ${A}^{m}(p)$ under $p\ensuremath{\rightarrow}\frac{1}{p}$. We then present a scalar field theory with a continuous parameter $\ensuremath{\xi}$ that reduces to the two previously discussed examples as special cases.
TL;DR: The Henneaux-Gibbons-Hawking-Stewart canonical measure on the set of classical universes is applied to a Friedmann-Robertson-Walker model containing a massive scalar field as mentioned in this paper.
TL;DR: In this paper, the authors investigated the behavior of particle detectors near straight strings in free space, immersed in thermal radiation, and passing through black holes and calculated the expectation values of the stress-energy-momentum tensor for a scalar field near straight string through black hole and in Robertson-Walker cosmological spacetimes.
Abstract: The gravitational field associated with cosmic strings can produce a variety of quantum field effects, such as vacuum polarisation and particle production. The authors investigate the behaviour of particle detectors near straight strings in free space, immersed in thermal radiation, and passing through black holes. The expectation values of the stress-energy-momentum tensor for a scalar field near straight strings through black holes and in Robertson-Walker cosmological spacetimes are also calculated.
TL;DR: An effective self-interaction for Goldstone bosons due to wormholes and child universes is shown to be a cosine potential, whose vacuum energy will be reduced by the cosmic expansion.
Abstract: The quantum theory of a complex scalar field coupled to gravity is considered. A formalism for the semiclassical approach in Euclidean time is developed and used to study wormhole physics. The conserved global charge plays an essential role. Wormhole physics turns on only after the symmetry is spontaneously broken. An effective self-interaction for Goldstone bosons due to wormholes is shown to be a cosine potential, whose vacuum energy will be reduced by the cosmic expansion. Some implications and questions are discussed.
TL;DR: Using the Korringa-Kohn-Rostoker method, the band structure for a classical scalar wave scattering from a periodic array of dielectric spheres in a uniform background is computed.
Abstract: Using the Korringa-Kohn-Rostoker method we compute the band structure for a classical scalar wave scattering from a periodic array of dielectric spheres in a uniform background. The optimal volume filling fraction $f$ of spheres for the creation of a total gap in the density of states, and hence localization, is found to be approximately 11%. This gap persists for refractive index ratios as small as 2.8.
TL;DR: In this article, the classical field theory of the interaction of cosmic strings is studied, and a limited survey of numerical evolutions has been carried out showing parallel string-string repulsion; string-antistring annihilation with initial velocity v = 0 and v=0.75; string−string collision at right angles with v/c= 0.9c, with v=π/4 and at θ=3π/ 4, and with v/(c=0,0.9) = 0.95.
Abstract: The putative ability of cosmic strings to act as seeds for galaxies depends on the efficiency of a number of processes that produce an initial network of strings and then allow them to evolve to a population that can act as condensation centers. Here the classical field theory of the interaction of cosmic strings is studied. A limited survey of numerical evolutions has been carried out. Calculations have been carried out showing parallel string–string repulsion; string–antistring (i.e., antiparallel string) annihilation with initial velocity v=0 and v=0.75; string–string collision at right angles with v/c=0.1, 0.5, 0.75, 0.85, 0.9c, with v/c=0.75 at θ=π/4 and at θ=3π/4, and with v/c=0.9 at θ=7π/8; and string–string and string–antistring collisions with v/c=0.9 and v/c=0.95. Intercommutation occurs in all situations so far investigated except that string–antistring collision with v/c≳0.90 apparently leads to reemergence, i.e., no intercommutation. All simulations have a ‘‘sombrero’’ potential V (φ)=λ(‖φ‖2−σ2)2 and a gauge field coupling e. (The numerical results are obtained with λ=0.01, e=0.2, giving the gauge field a slightly longer scale length than that of the scalar field.)
TL;DR: In this paper, an orthogonal series expansion for the three-dimensional joint probability density function (p.d.f.) is developed using the cumulants and Hermite polynomials.
Abstract: Various types of moments of velocity and scalar fluctuations of the first to the fourth order have been measured and analysed. First, an orthogonal series expansion for the three-dimensional joint probability density function (p.d.f.) is developed using the cumulants and Hermite polynomials. This p.d.f. is found to provide satisfactory predictions for the statistical characteristics, including triple products, of turbulent momentum and scalar transfer. Next, the conditional sampling and averaging technique is employed to investigate the statistical characteristics of coherent turbulent transfer processes of momentum and scalar. Conditional p.d.f.s are developed for various moments of velocity and scalar up to the third order. It is shown that the present p.d.f.s can predict the detailed role of coherent motions in the dynamics of wall turbulent shear flows and in the relevant process of scalar transport by turbulence. In particular, the importance of coherent motions in the turbulent diffusion process of Reynolds-stress components and scalar fluxes is demonstrated for the first time by the present theory.
TL;DR: In this paper, the authors considered the generation of initial perturbations in inflationary cosmological models in the presence of fluctuations of several scalar fields and showed that there is a possibility to build the model-dependent spectrum both of adiabatic (inflation) and isothermal (isoinflaton) density perturbation, containing a separate maximum, large-scale power or increasing at large (at small) wavelengths.
TL;DR: In this article, the authors considered the problem of soliton-antisoliton pair creation in a (1 + 1)-dimensional model of a real scalar field and showed that at certain temperatures, the soliton pair creation can be investigated by studying classical field evolution in real time.
TL;DR: In this article, the properties of different variants of parabolic approximations of scalar wave equations are analyzed, including those used in seismology, underwater acoustics and other applications.
Abstract: The properties of different variants of parabolic approximations of scalar wave equations are analyzed. These equations are of general form which includes those used in seismology, underwater acoustics and other applications. A new version of the parabolic approximation is derived for heterogeneous media. It has optimal properties with respect to wave reflection at material interfaces. The amplitudes of the reflected and transmitted waves depend continuously on the interface. Existence, uniqueness and energy estimates are proved.
TL;DR: In this article, the mean scalar, the scalar variance and the dissipation rate of scalar volumetric diffusion were modeled using a two-scale direct-interaction approximation.
Abstract: Modelling of turbulent passive-scalar diffusion is studied using the statistical results from a two-scale direct-interaction approximation. In this model, the mean scalar, the scalar variance and the dissipation rate of scalar variance constitute fundamental diffusion quantities. The turbulent scalar flux is written in the form of an anisotropic eddy-diffusivity representation. This representation, paving the way for explaining anisotropic heat transport, is tested against typical experimental data. The present model equation for the dissipation rate of scalar variance also gives a theoretical justification for the existing equations that are adopted in the second-order models.
TL;DR: In this article, the theories of a chiral spinor and real scalar superfield (scalar multiplet) in an external field of simple supergravity are considered, and the prescription for quantization is given, the quantum effective actions are constructed and quantum equivalence of the above-mentioned theories to the theory of a non-conformal chiral superfield is proved.
TL;DR: It is shown that the theory formulated is essentially equivalent to the one-loop field theory in de Sitter space and reduces to that of Starobinsky in a strong limit of the slow roll-over condition.
01 Jan 1988
TL;DR: In this paper, the decay of a false vacuum in a single scalar field with nonderivative interactions is studied. But the decay is not restricted to the case of singular fields.
Abstract: It is possible for a classical field theory to have two homogeneous stable equilibrium states with different energy densities. In the quantum version of the theory, the state of higher energy density becomes unstable through barrier penetration; it is a false vacuum. This is the first of two papers developing the qualitative and quantitative semiclassical theory of the decay of such a false vacuum for theories of a single scalar field with nonderivative interactions. In the limit of vanishing energy density between the two ground states, it is possible to obtain explicit expressions for the relevant quantities to leading order in $h$; in the more general case, the problem can be reduced to solving a single nonlinear ordinary differential equation.
TL;DR: In this article, the early stage of a new inflationary universe model with a Higgs-type potential was analyzed, and it was shown that quantum fluctuations play an important role for the dynamics of the scalar field as well as the classical potential force.