Ghost Modes Research Articles

A non-singular one-loop wave function of the universe from a new eigenvalue asymptotics in quantum gravity

Recent work on euclidean quantum gravity on the four-ball has proved regularity at the origin of the generalized ζ-function built from eigenvalues for metric and ghost modes, when diffeomorphism-invariant boundary conditions are imposed in the de Donder gauge. The hardest part of the analysis involves one of the four sectors for scalar-type perturbations, the eigenvalues of which are obtained by squaring up roots of a linear combination of Bessel functions of integer adjacent orders, with a coefficient of linear combination depending on the unknown roots. This paper obtains, first, approximate analytic formulae for such roots for all values of the order of Bessel functions. For this purpose, both the descending series for Bessel functions and their uniform asymptotic expansion at large order are used. The resulting generalized ζ-function is also built, and another check of regularity at the origin is obtained. For the first time in the literature on quantum gravity on manifolds with boundary, a vanishing one-loop wave function of the Universe is found in the limit of small three-geometry, which suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundary-value problem for one-loop quantum theory.

Comments on BRST quantization of strings

The BRST quantization of strings is revisited and the derivation of the path integral measure for scattering amplitudes is streamlined. Gauge invariances due to zero modes in the ghost sector are taken into account by using the Batalin-Vilkovisky formalism. This involves promoting the moduli of Riemann surfaces to quantum mechanical variables on which BRST transformations act. The familiar ghost and antighost zero mode insertions are recovered upon integrating out auxiliary fields. In contrast to the usual treatment, the gauge-fixed action including all zero mode insertions is BRST invariant. Possible anomalous contributions to BRST Ward identities due to boundaries of moduli space are reproduced in a novel way. Two models are discussed explicitly: bosonic string theory and topological gravity coupled to the topological A-model.

String theories with deformed energy-momentum relations, and a possible nontachyonic bosonic string

We consider a prescription for introducing deformed dispersion relations in the bosonic string action. We find that in a subset of such theories it remains true that the embedding coordinates propagate linearly on the world sheet. While both the string modes and the center of mass propagate with deformed dispersion relations, the speed of light remains energy independent. We consider the canonical quantization of these strings and find that it is possible to choose theories so that ghost modes still decouple, as usual. We also find that there are examples where the tachyon is eliminated from the spectrum of the free bosonic string.

Research on cylindrical box type windows used to transmit high power CW

The formula for calculating the threshold of average transmitting power of cylindrical TE11 mode window is revised by accurate deduction and a practical method for calculating the temperature increment of the dielectric disk in cylindrical box type window is given. Meanwhile, a typical cylindrical box type window is calculated and used as an example to discuss the power capacity, the special harmfulness and elimination of ghost mode resonance when the window is used to transmit high power Continuous Wave(CW).

Nonhydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations.

Lattice Boltzmann equations for the isothermal Navier-Stokes equations have been constructed systematically using a truncated moment expansion of the equilibrium distribution function from continuum kinetic theory. Applied to the shallow water equations, with its different equation of state, the same approach yields discrete equilibria that are subject to a grid scale computational instability. Different and stable equilibria were previously constructed by Salmon [J. Marine Res. 57, 503 (1999)]. The two sets of equilibria differ through a nonhydrodynamic or "ghost" mode that has no direct effect on the hydrodynamic behavior derived in the slowly varying limit. However, Salmon's equilibria eliminate a coupling between hydrodynamic and ghost modes, one that leads to instability with a growth rate increasing with wave number. Previous work has usually assumed that truncated moment expansions lead to stable schemes. Such instabilities have implications for lattice Boltzmann equations that simulate other nonideal equations of state, or that simulate fully compressible, nonisothermal fluids using additional particles.

ZERO-POINT ENERGY OF A CONDUCTING SPHERICAL SHELL

The zero-point energy of a conducting spherical shell is evaluated by imposing boundary conditions on the potential Aμ, and on the ghost fields. The scheme requires that temporal and tangential components of Aμ perturbations should vanish at the boundary, jointly with the gauge-averaging functional, first chosen to be of the Lorentz type. Gauge invariance of such boundary conditions is then obtained provided that the ghost fields vanish at the boundary. Normal and longitudinal modes of the potential obey an entangled system of eigenvalue equations, whose solution is a linear combination of Bessel functions under the above assumptions, and with the help of the Feynman choice for a dimensionless gauge parameter. Interestingly, ghost modes cancel exactly the contribution to the Casimir energy resulting from transverse and temporal modes of Aμ, jointly with the decoupled normal mode of Aμ. Moreover, normal and longitudinal components of Aμ for the interior and the exterior problem give a result in complete agreement with the one first found by Boyer, who studied instead boundary conditions involving TE and TM modes of the electromagnetic field. The coupled eigenvalue equations for perturbative modes of the potential are also analyzed in the axial gauge, and for arbitrary values of the gauge parameter. The set of modes which contribute to the Casimir energy is then drastically changed, and comparison with the case of a flat boundary sheds some light on the key features of the Casimir energy in noncovariant gauges.

Ghost modes and resonant effects in AlGaN-InGaN-GaN lasers

Many diode laser structures, including those based on group-III nitride system, contain passive waveguide layers of higher refractive index than in the adjacent layers. Modes of such passive waveguides ("passive" modes) can interact with an active layer mode ("active" mode), giving rise to two kinds of normal modes or "supermodes" of a laser structure. Away from resonance, one of them is localized predominantly in the active region ("lasing" mode), while the other ones are located mostly in passive waveguides ("ghost" modes). The lasing mode is the mode at which laser generation occurs. The lossy ghost modes are parasitic modes of a laser structure that can consume energy from the active region. Resonant coupling occurs when the lasing mode and a ghost mode are in phase synchronism. In the paper, the concept of ghost modes is applied to InGaN-based diode lasers. The values for critical thickness are calculated for p-GaN cap layer and for n-GaN buffer/substrate layer for a particular multilayer laser structure. The typical thickness of 0.5 /spl mu/m of AlGaN-cladding layer is found to be insufficient to prevent rather strong coupling between the modes. Under the resonant coupling conditions, the modal gain is shown to be strongly suppressed, allowing no lasing at all.

Axial gauge in Euclidean quantum gravity

The axial gauge is applied to the analysis of Euclidean quantum gravity on manifolds with boundary. A set of boundary conditions which are completely invariant under infinitesimal diffeomorphisms require that spatial components of metric perturbations should vanish at the boundary, jointly with all components of the ghost one-form and of the gauge-averaging functional. If the latter is taken to be of the axial type, all components of metric perturbations obey Dirichlet conditions, and all ghost modes are forced to vanish identically. The one-loop divergence coincides with the contribution resulting from three-dimensional transverse-traceless perturbations.

Noncovariant Gauges in Simple Supergravity

A gauge-averaging functional of the axial type is studied for simple supergravity at one loop about flat Euclidean four-space bounded by a three-sphere, or two concentric three-spheres. This is a generalization of recent work on the axial gauge in quantum supergravity on manifolds with boundary. Ghost modes obey nonlocal boundary conditions of the spectral type, in that half of them obey Dirichlet or Neumann conditions at the boundary. In both cases, they give a vanishing contribution to the one-loop divergence. The admissibility of noncovariant gauges at the classical level is also proved.

One-loop effective action for Euclidean Maxwell theory on manifolds with a boundary.

This paper studies the one-loop effective action for Euclidean Maxwell theory about flat four-space bounded by one three-sphere, or two concentric three-spheres. The analysis relies on the Faddeev-Popov formalism and $\ensuremath{\zeta}$-function regularization, and the Lorentz gauge-averaging term is used with magnetic boundary conditions. The contributions of transverse, longitudinal, and normal modes of the electromagnetic potential, jointly with ghost modes, are derived in detail. The most difficult part of the analysis consists in the eigenvalue condition given by the determinant of a 2\ifmmode\times\else\texttimes\fi{}2 or a 4\ifmmode\times\else\texttimes\fi{}4 matrix for longitudinal and normal modes. It is shown that the former splits into a sum of Dirichlet and Robin contributions, plus a simpler term. This is the quantum-cosmological case. In the latter case, however, when magnetic boundary conditions are imposed on two bounding three-spheres, the determinant is more involved. Nevertheless, it is evaluated explicitly as well. The whole analysis provides the building block for studying the one-loop effective action in covariant gauges, on manifolds with boundary. The final result differs from the value obtained when only transverse modes are quantized, or when noncovariant gauges are used.

Local boundary conditions in quantum supergravity

When quantum supergravity is studied on manifolds with boundary, one may consider local boundary conditions which fix on the initial surface the whole primed part of tangential components of gravitino perturbations, and fix on the final surface the whole unprimed part of tangential components of gravitino perturbations. This paper studies such local boundary conditions in a flat Euclidean background bounded by two concentric 3-spheres. It is shown that, as far as transverse-traceless perturbations are concerned, the resulting contribution to ζ(0) vanishes when such boundary data are set to zero, exactly as in the case when non-local boundary conditions of the spectral type are imposed. These properties may be used to show that one-loop finiteness of massless supergravity models is only achieved when two boundary 3-surfaces occur, and there is no exact cancellation of the contributions of gauge and ghost modes in the Faddeev-Popov path integral. In these particular cases, which rely on the use of covariant gauge-averaging functionals, pure gravity is one-loop finite as well.

One-loop divergences in simple supergravity: Boundary effects.

This paper studies the semiclassical approximation of simple supergravity in Riemannian four-manifolds with a boundary, within the framework of $\ensuremath{\zeta}$-function regularization. The massless nature of gravitinos, jointly with the presence of a boundary and a local description in terms of potentials for spin 3/2, force the background to be totally flat. First, nonlocal boundary conditions of the spectral type are imposed on spin-3/2 potentials, jointly with boundary conditions on metric perturbations which are completely invariant under infinitesimal diffeomorphisms. The axial gauge-averaging functional is used, which is then sufficient to ensure self-adjointness. One, thus, finds that the contributions of ghost and gauge modes vanish separately. Hence the contributions to the one-loop wave function of the universe reduce to those $\ensuremath{\zeta}(0)$ values resulting from physical modes only. Another set of mixed boundary conditions, motivated instead by local supersymmetry and first proposed by Luckock, Moss, and Poletti, is also analyzed. In this case the contributions of gauge and ghost modes do not cancel each other. Both sets of boundary conditions lead to a nonvanishing $\ensuremath{\zeta}(0)$ value, and spectral boundary conditions are also studied when two concentric three-sphere boundaries occur. These results seem to point out that simple supergravity is not even one-loop finite in the presence of boundaries.

1-loop effective action on the 4-ball

This paper applies -function regularization to evaluate the 1-loop effective action for scalar field theories and Euclidean Maxwell theory in the presence of boundaries. After a comparison of two techniques developed in the recent literature, the vacuum Maxwell theory is studied and the contribution of all perturbative modes to is derived: transverse, longitudinal and normal modes of the electromagnetic potential, jointly with ghost modes. The analysis is performed by imposing magnetic boundary conditions, when the Faddeev - Popov Euclidean action contains the particular gauge-averaging term which leads to a complete decoupling of all perturbative modes. It is shown that there is no cancellation of the contributions to resulting from longitudinal, normal and ghost modes.

One-loop amplitudes in Euclidean quantum gravity.

This paper studies the linearized gravitational field in the presence of boundaries. For this purpose, $\zeta$-function regularization is used to perform the mode-by-mode evaluation of BRST-invariant Faddeev-Popov amplitudes in the case of flat Euclidean four-space bounded by a three-sphere. On choosing the de Donder gauge-averaging term, the resulting $\zeta(0)$ value is found to agree with the space-time covariant calculation of the same amplitudes, which relies on the recently corrected geometric formulas for the asymptotic heat kernel in the case of mixed boundary conditions. Two sets of mixed boundary conditions for Euclidean quantum gravity are then compared in detail. The analysis proves that one cannot restrict the path-integral measure to transverse-traceless perturbations. By contrast, gauge-invariant amplitudes are only obtained on considering from the beginning all perturbative modes of the gravitational field, jointly with ghost modes.

Gravitons in one-loop quantum cosmology: Correspondence between covariant and noncovariant formalisms.

The discrepancy between the results of covariant and noncovariant one-loop calculations for higher-spin fields in quantum cosmology is analyzed. A detailed mode-by-mode study of perturbative quantum gravity about a flat Euclidean background bounded by two concentric three-spheres, including nonphysical degrees of freedom and ghost modes, leads to one-loop amplitudes in agreement with the covariant Schwinger-DeWitt method. This calculation provides the generalization of a previous analysis of fermionic fields and electromagnetic fields at one-loop about flat Euclidean backgrounds admitting a well-defined 3+1 decomposition.

Remarks on theoretical problems in nonsymmetric gravitational theory.

Damour, Deser and McCarthy have claimed that the nonsymmetric gravitational theory (NGT) is untenable due to curvature coupled ghost modes and bad asymptotic behavior. This claim is false for it is based on a physically inaccurate treatment of wave propagation on a curved background and an incorrect method for extracting asymptotic behavior. We show that the flux of gravitational radiation in NGT is finite in magnitude and positive in sign.

Theoretical problems in nonsymmetric gravitational theory.

It has recenty been noted that the nonsymmetric metric model of gravity faces severe observational constraints. We show here that it is also subject to physically unacceptable formal difficulties even as an effective field theory: When expanded about a Riemannian background, the model exhibits curvature-coupled negative-energy (ghost) modes and unacceptable asymptotic behavior.

The big picture

We discuss the conformal field theory and string field theory of the NSR superstring using a BRST operator with a non-minimal term, which allows all bosonic ghost modes to be paired into creation and annihilation operators. Vertex operators for the Neveu-Schwarz and Ramond sectors have the same ghost-number, as do string fields. The kinetic and interaction terms are the same for Neveu-Schwarz as for Ramond string fields, so space-time supersymmetry is closer to being manifest. The kinetic terms and supersymmetry do not mix levels, simplifying component a analysis and gauge fixing.

Spectral boundary conditions in one-loop quantum cosmology.

For fermionic fields on a compact Riemannian manifold with a boundary, one has a choice between local and nonlocal (spectral) boundary conditions. The one-loop prefactor in the Hartle-Hawking amplitude in quantum cosmology can then be studied using the generalized Riemann $\ensuremath{\zeta}$ function formed from the squared eigenvalues of the four-dimensional fermionic operators. For a massless Majorana spin-\textonehalf{} field, the spectral conditions involve setting to zero half of the fermionic field on the boundary, corresponding to harmonics of the intrinsic three-dimensional Dirac operator on the boundary with positive eigenvalues. Remarkably, a detailed calculation for the case of a flat background bounded by a three-sphere yields the same value $\ensuremath{\zeta}(0)=\frac{11}{360}$ as was found previously by the authors using local boundary conditions. A similar calculation for a spin-$\frac{3}{2}$ field, working only with physical degrees of freedom (and, hence, excluding gauge and ghost modes, which contribute to the full Becchi-Rouet-Stora-Tyutininvariant amplitude), again gives a value $\ensuremath{\zeta}(0)=\ensuremath{-}\frac{289}{360}$ equal to that for the natural local boundary conditions.

Anomalous shifts of oxygen-mode frequencies inLa2−xSrxCuO4,YBa2Cu3O7−δandTl2Ba2Ca1−xGdxCu2O8studied by photoinduced infrared absorption and Raman spectroscopy

Comparison of photoinduced local modes (PILM's) of insulating ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.3}$ and ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Gd}}_{\mathit{x}}$${\mathrm{Cu}}_{2}$${\mathrm{O}}_{8}$ with Raman spectra of their metallic counterparts suggests that carrier injection anomalously increases the frequencies of phonons involving z-axis apex-oxygen motion in both the dilute (insulator) and concentrated (metallic) limit. In ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$, we observe PILM's whose frequencies suggest a correspondence with the ``ghost modes'' observed in neutron scattering [Rietschel et al., Physica C 162--164, 1705 (1989)]. These data, together with Raman data on apex-oxygen anharmonicity, enable us to discuss the vibronic mode couplings involved in polaron formation in the three materials.