Showing papers on "Scalar field published in 1978"
TL;DR: A renormalization ansatz based on the DeWitt-Schwinger expansion is proposed, and it is shown that this removes all am biguities previously present in pointsplitting regularization.
Abstract: We examine the modes of a scalar field in de Sitter space and construct quantum two-point functions. These are then used to compute a finite stress tensor by the technique of covariant point-splitting. We propose a renormalization ansatz based on the DeWitt-Schwinger expansion, and show that this removes all am biguities previously present in pointsplitting regularization. The results agree in detail with previous work by dimensional regularization, and give rise to an anomalous trace with the conventional coefficient. We describe how’ our treatment may be extended to more general situations.
1,125 citations
CERN1
TL;DR: For a wide class of Euclidean scalar field equations, there exist non-trivial solutions as mentioned in this paper, and the solution of the lowest action is spherically symmetric.
Abstract: We show that for a wide class of Euclidean scalar field equations, there exist non-trivial solutions, and the non-trivial solution of lowest action is spherically symmetric. This fills a gap in a recent analysis of vacuum decay by one of us.
476 citations
CERN1
TL;DR: In this article, the minimal set of auxiliary fields of supergravity is defined, needed to close the supergravity algebra, and the invariant action is shown to be invariant to a scalar, a pseudoscalar and a world vector field.
360 citations
TL;DR: In this article, it was shown that if a scalar field has the Hadamard singularity structure in an open neighborhood of a Cauchy surface, then it does so everywhere.
Abstract: In the point-splitting prescription for renormalizing the stress-energy tensor of a scalar field in curved spacetime, it is assumed that the anticommutator expectation valueG(x, x′)=〈o(x)o(x′)+o(x′)o(x)〉 has a singularity of the Hadamard form asx→x′. We prove here that ifG(x,x′) has the Hadamard singularity structure in an open neighborhood of a Cauchy surface, then it does so everywhere, i.e., Cauchy evolution preserves the Hadamard singularity structure. In particular, in a spacetime which is flat below a Cauchy surface, for the “in” vacuum stateG(x,x′) is of the Hadamard form everywhere, and thus the point-splitting prescription in this case has been rigorously shown to give meaningful, finite answers.
239 citations
TL;DR: The recent general solution by Atiyah, Hitchin, Drinfeld, and Manin of the self-duality equations for an arbitrary compact classical group is discussed in this article, where the Green function for a scalar field transforming as a vector under the group is shown to take an elegant form in the background field of the general selfdual solution and massless solutions of the Dirac equation for this representation of the group are also explicitly exhibited.
171 citations
TL;DR: In this paper, it was shown that for widely separated instantons this equation can be solved perturbatively, providing a systematic expansion about the dilute-gas limit and a physical interpretation of the independent parameters in this limit.
Abstract: The recent work of Atiyah, Hitchin, Drinfeld, and Manin is used to discuss self-dual Yang-Mills solutions for the compact gauge groups $O(n)$, $\mathrm{SU}(n)$, and $\mathrm{Sp}(n)$. It is shown that the resulting solutions contain the correct number of parameters for all values of the topological charge. Although explicit construction of a general self-dual field requires the solution of a finite-dimensional, nonlinear matrix equation, we show that for widely separated instantons this equation can be solved perturbatively, providing a systematic expansion about the dilute-gas limit and a physical interpretation of the independent parameters in this limit. Further, closed-form expressions can be obtained for the general SU(2) solutions with topological charge 2 or 3. Finally, explicit isospin-1/2 and isospin-1 propagators are derived for a massless scalar field in the presence of the general self-dual SU(2) solution.
160 citations
TL;DR: In this article, a quantized field in a Bianchi type-I anisotropic expanding universe is considered, and boundary conditions are imposed at an initial time t/sub 0/ of the order of the Planck time with the initial expansion rates varying over a wide range consistent with the constraints.
Abstract: We consider a quantized field in a Bianchi type-I anisotropically expanding universe. A suitable expectation value of the renormalized energy-momentum tensor acts as the source of the metric in the Einstein equations. The coupled set of differential equations is numerically integrated, with the help of several approximations, in the case when the quantized field is the massless conformal scalar field. Boundary conditions are imposed at an initial time t/sub 0/ of the order of the Planck time, with the initial expansion rates varying over a wide range consistent with the constraints. It is found that the expansion rates tend toward isotropy and approach a radiation-filled Friedman expansion in an interval of less than 10/sup 3/ Planck times, for the full range of initial expansion rates considered.
156 citations
TL;DR: In this paper, the force and torque on a molecule can be derived, as V function expansions, from a potential given in S function form, and the necessary formulae are listed.
Abstract: Any scalar function of the orientation of a pair of molecules, of arbitrary shape, can be expanded in terms of a complete orthogonal set of functions called S functions. Any vector function can similarly be expanded in terms of V functions. Although the functions are expressed in terms of Wigner rotation matrices, they can be evaluated efficiently enough for use in molecular dynamics calculations. In particular, trigonometrical function evaluations are not required. The force and torque on a molecule can be derived, as V function expansions, from a potential given in S function form, and the necessary formulae are listed.
149 citations
TL;DR: In this paper, the authors give mathematically rigorous results on the quantization of the covariant Klein Gordon field with an external stationary scalar interaction in astationary curved space-time.
Abstract: . We give mathematically rigorous results on the quantization of thecovariant Klein Gordon field with an external stationary scalar interaction in astationary curved space-time.We show how, following Segal, Weinless etc., the problem reduces tofinding a "one particle structure" for the corresponding classical system.Our main result is an existence theorem for such a one-particle structure fora precisely specified class of stationary space-times. Byproducts of ourapproach are:1) A discussion of when a given "equal-lime" surface in a given stationaryspace-time is Cauchy.2) A modification and extension of the methods of Chernoff [3] forproving the essential self-adjointness of certain partial differential operators. §0. Introduction In this series of papers, we discuss the quantization of the equation V)φ = Q, (0.1)— the covariant Klein Gordon equation in a fixed curved space-time (.,//, g μv ) and interacting with a fixed external scalar field V. (We shall always take (.,//,
147 citations
TL;DR: The second form is in general parity non-conserving, while both forms have scalar field potentials that are unbounded from below as discussed by the authors, and is indeed inequivalent to the first form.
147 citations
TL;DR: In this paper, the authors proved that black holes with a conformal scalar field are unstable under monopole perturbations, and proved that the same is true for a black hole with a non-convex scalar force.
TL;DR: In this article, the vacuum-averaged stress energy tensor is calculated for a scalar field on a variety of static space-times, T(X)M3, where the spatial section, M3, is a Clifford-Klein space form of the flat or spherical type, R3/Gamma, or S3/ Gamma.
Abstract: The vacuum-averaged stress-energy tensor is calculated for a scalar field on a variety of static space-times, T(X)M3, where the spatial section, M3, is a Clifford-Klein space form of the flat or spherical type, R3/ Gamma , or S3/ Gamma . The particular examples when M3 is a Klein-bottle waveguide, R(X)K2, or a lens-space, S3/Zm, are treated in most detail. It is found that the vacuum stress on quotient spaces is not of the same tensorial structure as Rmu nu -1/2gmu nu R. This leads to difficulties with the back-reaction problem. It is further found that 'twisting' the field alters the vacuum stress compared to the untwisted theory. Values for the total energies in the three types of polyhedral cellular decompositions of S3 are given. Dirichlet boundary conditions for rectangular cavities are also considered.
TL;DR: In this article, the Lagrangian density for interacting electromagnetic, gravitational, torsion, and complex scalar fields is presented, as well as the resulting field equations, which imply the existence of both electric and magnetic currents due to the interaction of the electromagnetic and Torsion fields.
Abstract: A formalism is given which makes it possible for a modified form of local gauge invariance and minimal coupling to be compatible with torsion. One consequence is a restriction on the possible form of torsion in that it must be determined by the gradient of a scalar function. Furthermore, a dynamical theory is obtained for this scalar and hence allows propagation of torsion in vacuum. The Lagrangian density for interacting electromagnetic, gravitational, torsion, and complex scalar fields is presented, as well as the resulting field equations. The formalism implies the existence of both electric and magnetic currents due to the interaction of the electromagnetic and torsion fields.
TL;DR: In this paper, the authors considered linear perturbations of black hole models by a variety of fields and derived the crucial condition th at the field be singular on the inner horizon.
Abstract: Linear perturbations of black hole models by a variety of fields are considered. Perturbing fields include the zero rest mass scalar field in the case of Reissner-Nordstrom, and gravitational, electromagnetic and zero rest mass scalar perturbation in the case of the Kerr model. The analysis deals with the Ψ 0 components (in the Newman-Penrose (1962) formalism) of non-zero spin fields. The symmetry properties of the models are used to derive the crucial condition th at the field be singular on the inner horizon. This condition is independent of the field propagation equation. Initial data are then given in terms of incoming radiation from f - is shown that there exist wellbehaved initial data sets for which the resultant fields are singular on the inner horizon. It is emphasized that this instability result is dependent only on the global symmetries and causal structure of the models considered, and is independent of the precise nature of the perturbing field.
TL;DR: In this paper, the authors calculate eigenfrequencies (including e-folding times) for stable and unstable modes of a scalar field on a background metric which has an ergoregion.
Abstract: Rotating, ultra-compact stars in general relativity can have an ergoregion, in which all trajectories are dragged in the direction of the star's rotation. The existence of the ergoregion leads to a classical instability to emission of scalar, electromagnetic and gravitational radiation from the star. In this paper we calculate eigenfrequencies (including e-folding times) for stable and unstable modes of a scalar field on a background metric which has an ergoregion. Within a W.K.B.J. approximation for modes with angular dependence exp (imo), we find that unstable modes exist for all ImI > mo (mi depending upon the star), but that the e-folding time is asymptotically r = ro exp (2flm), where ,8 is of order 1. Typically, T0 is several orders of magnitude longer than the age of the universe. However, the techniques evolved here should be applicable to other 'rotational dragging' instabilities in general relativity. Particularly useful should be the result that links the eigenfrequencies to resonances in the effective potentials governing photon motion in the metric; these potentials are rotationally 'split'.
TL;DR: In this paper, a time-independent spherically symmetric solution of general-relativistic nonlinear field equations is obtained, which can be regarded as a three-dimensional extension of the usual kink solution on the generalized spatial topology.
Abstract: A time-independent spherically symmetric solution of general-relativistic nonlinear field equations is obtained. It is shown that the nonlinear negative-energy scalar field has a localized solution with a positive mass. Wheeler's wormhole-type geometry is generated by the field. It can be regarded as a three-dimensional extension of the usual kink solution on the generalized spatial topology, connecting the two vacuum states from one asymptotically flat space to the other through the Rosen-Einstein bridge. The solution is shown to be completely singularity-free.
TL;DR: In this article, the authors derived the Davies-Fulling-Unruh expression for the stress tensor of a scalar field in conformally flat spacetimes of two and four dimensions.
TL;DR: In this paper, the authors examined the question of whether black holes can have associated external massive vector and/or scalar fields, when the masses are produced by spontaneous symmetry breaking.
Abstract: We examine the question of whether black holes can have associated external massive vector and/or scalar fields, when the masses are produced by spontaneous symmetry breaking. Working throughout in the spherically symmetric case, we show that "no-hair" theorems can be proved for the vector field in the Abelian Higgs model, for an arbitrary $\ensuremath{\xi}R{|\ensuremath{\varphi}|}^{2}$ term in the Higgs Lagrangian, and for the Goldstone scalar field model with $\ensuremath{\xi}=0$. We also show that a Minkowski-space analog problem does have nontrivial screened charge solutions, indicating that the "no-hair" theorems which we prove are consequences of the stringent conditions at the assumed horizon in the general-relativistic case, not of the interacting field or spontaneous-symmetry-breaking aspects of the problem.
TL;DR: In this paper, the creation of massless scalar particles by naked singularities in asymptotically flat spacetimes is investigated within the geometrical-optics approximation.
Abstract: The creation of massless scalar particles by naked singularities in asymptotically flat spacetimes is investigated within the geometrical-optics approximation. To avoid the need to impose boundary conditions on the singularity, we consider models in which a curvature singularity arises at a finite time in the past. We consider two particular types of models. One is a shell-crossing singularity formed in the gravitational collapse of a dust cloud. The energy flux of the created particles remains finite up to the time of formation of the singularity. In the particular case when the singularity forms on the event horizon, geometrical optics yields the exact flux, in spite of the high curvature of spacetime. The radiation obtained is identical to the thermal Hawking radiation emitted by black holes. The other models considered are those of charged shells for which the charge exceeds the mass. If these shells collapse to form naked singularities (which is possible if the proper mass is negative or if Einstein's equations are not imposed), an infinite flux of created particles results. In the cases examined here, the flux is negative for two-dimensional models and for the minimally coupled scalar field in four-dimensional models, whereas it is positive for the conformally coupled scalar field in four-dimensional models. In either case, the back reaction from particle creation will be large and may prevent formation of a naked singularity.
TL;DR: In this article, the authors considered general scalar perturbations of a Reissner-Nordstrom black hole and examined the qualitative behaviour of these perturbation in the region between and on the inner and outer horizons.
Abstract: This paper considers general scalar perturbations of a Reissner-Nordstrom black hole and examines the qualitative behaviour of these perturbations in the region between and on the inner and outer horizons $r\_{-}$ $\leq $ $r\leq $ $r\_{+}$. Initial data are specified in terms of the ingoing radiation crossing the outer (event) horizon. The only essential restriction on these data is that the radiation should not die away too slowly on this horizon. The resultant perturbations are shown to be bounded and continuous. It is also shown that if $\tilde{u}$ is any retarded null coordinate such that $\tilde{u}$ = 0 on the event horizon, then the perturbations tend to zero along lines of constant radius as $\tilde{u}$ $\downarrow $ 0. In particular, all these properties hold for perturbations on the inner horizon. For certain types of scalar field (including the zero rest mass scalar field) perturbations vanish at the crossover point on the inner horizon.
TL;DR: The renormalization ansatz suggested by these expansions can be implemented at the integrand level for practical computations as discussed by the authors, which is applicable to four-dimensional models, and has been shown to be conservable in the two-dimensional "Milne universe" (flat space in hyperbolic coordinates).
Abstract: The stress tensor of a massive scalar field, as an integral over normal modes (which are not mere plane waves), is regularized by covariant point separation. When the expectation value in a Parker-Fulling adiabatic vacuum state is expanded in the limit of small curvature-to-mass ratios, the series coincides in each order with the Schwinger-DeWitt-Christensen proper-time expansion. The renormalization ansatz suggested by these expansions (which applies to arbitrary curvature-to-mass ratios and arbitrary quantum state) can be implemented at the integrand level for practical computations. The renormalized tensor (1) passes in the massless limit, for appropriate choice of state, to the known vacuum stress of a massless field, (2) agrees with the explicit results of Bernard and Duncan for a special model, and (3) has a nonzero vacuum expectation value in the two-dimensional ''Milne universe'' (flat space in hyperbolic coordinates). Following Wald, we prove that the renormalized tensor is conserved and point out that there is no arbitrariness in the renormalization procedure. The general approach of this paper is applicable to four-dimensional models.
TL;DR: In this paper, the ground state of a twisted scalar field on a two-dimensional Einstein cylinder is studied and the authors show that there is a spontaneous breakdown of the spatial translational invariance of the twisted ground state as a characteristic length increases across a critical value.
Abstract: The properties of the ground state of a classical self-interacting twisted scalar field on a two-dimensional Einstein cylinder are discussed. In particular there is a spontaneous breakdown of the spatial translational invariance of the twisted ground state as a characteristic length increases across a critical value. Similar properties are shown to hold in a four-dimensional model. Finally, it is shown that there exist four-dimensional models which do not have any finite-energy twisted scalar fields.
TL;DR: In this paper, a vectorial wave analysis of the propagation characteristics of radially inhomogeneous optical fibers is presented, which is first translated into a variational problem and then solved by using the finite element method.
Abstract: A vectorial wave analysis of the propagation characteristics of radially inhomogeneous optical fibers is presented. The vectorial wave equation is first translated into a variational problem, and then it is solved by using the finite element method. The results are compared with those of the scalar wave analysis. The error caused by the scalar wave approximation is discussed for wide variety of refractive index profiles. It is shown that the error caused by the scalar wave approximation is about 0.1 percent for eigenvalues and 1 percent for delay time, when the relative index difference between core and cladding is 1 percent.
TL;DR: In this paper, the exact solutions of the radial equation valid over the 'whole range' can be found-unlike the corresponding situation in the Schwarzschild spacetime, and the power spectrum of Hawking radiation is evaluated after calculating the absorption probability at the horizon.
Abstract: The time dependent wave equation for a conformally coupled massless scalar field in a de Sitter universe is examined. It is pointed out that the exact solutions of the radial equation valid over the 'whole range' can be found-unlike the corresponding situation in the Schwarzschild spacetime. The power spectrum of Hawking radiation is evaluated after calculating the absorption probability at the horizon. The solution is seen to be well behaved at the origin.
TL;DR: In this article, a conformally coupled massless scalar field in two-and four-dimensional Robertson-Walker space-times was used to obtain the vacuum expectation value of the stress tensor.
Abstract: Adiabatic regularisation is used to obtain the vacuum expectation value of the stress tensor for a conformally coupled massless scalar field in two- and four-dimensional Robertson-Walker space-times. The results obtained agree with previous work using point-splitting (including the accepted value for the anomalous trace) but the details of the calculation are very much simpler and more elegant.
TL;DR: In this paper, the expectation value of the renormalized stress tensor for a conformally coupled massless scalar field propagating in an arbitrary hyperbolic Robertson-Walker spacetime is calculated.
Abstract: The vacuum expectation value of the renormalized stress tensor for a conformally coupled massless scalar field propagating in an arbitrary hyperbolic Robertson-Walker spacetime is calculated. The vacuum state used is that obtained by conformal transformation to the static hyperbolic universe: The result differs from calculations performed using the vacuum defined by conformal transformation to Minkowski spacetime, and is also different from earlier results obtained using the conformally static vacuum which are shown to be incorrect.
TL;DR: In this article, the authors investigated closed-vortex configurations in classical field theory and showed that such configurations are unstable by collapse in the Abelian Higgs model and constructed closed-ring configurations having unit Hopf index and that explicitly exhibit the features of a twisted vortex.
Abstract: Closed-vortex configurations in classical field theory are investigated here. It is shown in detail that in the Abelian Higgs model such configurations are unstable by collapse. Closed-ring configurations having unit Hopf index and that explicitly exhibit the features of a twisted vortex are constructed for theories where a three-component scalar field is present. However, it is shown that in renormalizable theories the Hopf charge does not ensure the existence of stable solutions. It is proved that a nonlinear $\ensuremath{\sigma}$ model where an interaction which has fourth-power field derivatives is present has a twisted-ring solution. A lower bound for the mass and estimates for the radius and mass are given.
TL;DR: In this paper, the authors derived formulas relating to coherence and radiant intensity in fields generated by primary sources in terms of a source correlation function, and showed the connection between the field description and the source description.
Abstract: In the literature on coherence theory one almost invariably specifies any correlations that may exist in the source region by means of a correlation function of the field variable. However, when the source is a primary one, it seems more appropriate to specify the correlations by means of a correlation function of the source variable. In the present paper some basic formulas are derived, relating to coherence and radiant intensity in fields generated by primary sources in terms of a source correlation function. A number of results are obtained that exhibit the connection between the “field description” and the “source description.” Several illustrative examples are given relating to Gaussian-correlated sources and to Lambertian sources.
TL;DR: In this article, a solution to the scalar wave equation in the Godel universe is presented in terms of exponential and associated Laguerre functions, where the frequency spectrum of the perturbations is bounded from below by twice the rotation frequency of the universe, and for fixed wave number in a certain spatial direction, it is also quantized.
Abstract: Solutions to the classical scalar wave equation in the Godel universe are constructed and their properties investigated. The solutions can be expressed in closed form in terms of exponential and associated Laguerre functions. The frequency spectrum of the perturbations is bounded from below by twice the rotation frequency of the universe, and, for fixed wave number in a certain spatial direction, it is also quantized. The scalar perturbations are compared to the electromagnetic perturbations studied by Mashhoon, and an attempt is made to geometrically interpret the frequency quantization.
TL;DR: In this article, the authors give a construction for multiple meron-antimeron solutions to the classical SU(2) Yang-Mills field equations, where the corresponding charge density is Q(x) = 1 2 ∑ ± γ(x−x i ), with the xi distinct points on a line.