102 research outputs found

    Late Holocene relative sea levels near Palmer Station, northern Antarctic Peninsula, strongly controlled by late Holocene ice-mass changes

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    Many studies of Holocene relative sea-level (RSL) changes across Antarctica assume that their reconstructions record uplift from glacial isostatic adjustment caused by the demise of the Last Glacial Maximum (LGM) ice sheets. However, recent analysis of GPS observations suggests that mantle viscosity beneath the Antarctic Peninsula is weaker than previously thought, which would imply that solid Earth motion is not controlled by post-LGM ice-sheet retreat but instead by late Holocene ice-mass changes. If this hypothesis is correct, one might expect to find Holocene RSL records that do not reflect a monotonic decrease in the rate of RSL fall but show variations in the rate of RSL change through the Holocene. We present a new record of late Holocene RSL change from Torgersen Island near Palmer Station in the western Antarctic Peninsula that shows an increase in the rate of relative sea-level fall from 3.0 ± 1.2 mm/yr to 5.1 ± 1.8 mm/yr during the late Holocene. Independent studies of the glacial history of the region provide evidence of ice-sheet changes over similar time scales that may be driving this change. When our RSL records are corrected for sea-surface height changes associated with glacial isostatic adjustment (GIA), the rate of post-0.79 ka land uplift at Torgersen Island, 5.3 ± 1.8 mm/yr, is much higher than the rate of uplift recorded at a nearby GPS site at Palmer Station prior to the Larsen B breakup in 2002 AD (1998-2002 AD; <0.1 mm/yr), but similar to the rates observed after 2002 AD (2002-2013 AD; 6–9 mm/yr). This substantial variation in uplift rates further supports the hypothesis that Holocene RSL rates of change are recording responses to late Holocene and recent changes in local ice loading rather than a post-LGM signal across portions of the Antarctic Peninsula. Thus middle-to-late Holocene RSL data may not be an effective tool for constraining the size of the LGM ice sheet across portions of the Antarctic Peninsula underlain by weaker mantle. In addition, current global-scale GIA models are unable to predict our observed changes in late Holocene RSL. Complexities in Earth structure and neoglacial history need to be taken into consideration in GIA models used for correcting modern satellite-based observations of ice-mass loss

    The renormalization of the effective Lagrangian with spontaneous symmetry breaking: the SU(2) case

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    We study the renormalization of the nonlinear effective SU(2) Lagrangian up to O(p4)O(p^4) with spontaneous symmetry breaking. The Stueckelberg transformation, the background field gauge, the Schwinger proper time and heat kernel method, and the covariant short distance expansion technology, guarantee the gauge covariance and incooperate the Ward indentities in our calculations. The renormalization group equations of the effective couplings are derived and analyzed. We find that the difference between the results gotten from the direct method and the renormalization group equation method can be quite large when the Higgs scalar is far below its decoupling limit.Comment: ReVTeX, 12 figures, 22 pages, some bugs are kicked off from programs, numerical analysis is renew

    Quantum Yang-Mills gravity in flat space-time and effective curved space-time for motions of classical objects

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    Yang-Mills gravity with translational gauge group T(4) in flat space-time implies a simple self-coupling of gravitons and a truly conserved energy-momentum tensor. Its consistency with experiments crucially depends on an interesting property that an `effective Riemannian metric tensor' emerges in and only in the geometric-optics limit of the photon and particle wave equations. We obtain Feynman rules for a coupled graviton-fermion system, including a general graviton propagator with two gauge parameters and the interaction of ghost particles. The equation of motion of macroscopic objects, as an N-body system, is demonstrated as the geometric-optics limit of the fermion wave equation. We discuss a relativistic Hamilton-Jacobi equation with an `effective Riemann metric tensor' for the classical particles.Comment: 20 pages, to be published in "The European Physical Journal - Plus"(2011). The final publication is available at http://www.epj.or

    On Relativistic Material Reference Systems

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    This work closes certain gaps in the literature on material reference systems in general relativity. It is shown that perfect fluids are a special case of DeWitt's relativistic elastic media and that the velocity--potential formalism for perfect fluids can be interpreted as describing a perfect fluid coupled to a fleet of clocks. A Hamiltonian analysis of the elastic media with clocks is carried out and the constraints that arise when the system is coupled to gravity are studied. When the Hamiltonian constraint is resolved with respect to the clock momentum, the resulting true Hamiltonian is found to be a functional only of the gravitational variables. The true Hamiltonian is explicitly displayed when the medium is dust, and is shown to depend on the detailed construction of the clocks.Comment: 18 pages, ReVTe

    Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral

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    The DeWitt expansion of the matrix element M_{xy} = \left\langle x \right| \exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle, (p=i)(p=-i\partial) in powers of tt can be made in a number of ways. For x=yx=y (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when xyx \neq y (relevant for doing calculations beyond one-loop) there appear to be but two examples of performing the DeWitt expansion. In this paper we compute the off-diagonal elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge. Our technique is based on representing MxyM_{xy} by a quantum mechanical path integral. We also generalize our method to the case of curved space, allowing us to determine the DeWitt expansion of \tilde M_{xy} = \langle x| \exp \case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle by use of normal coordinates. By comparison with results for the DeWitt expansion of this matrix element obtained by the iterative solution of the diffusion equation, the relative merit of different approaches to the representation of M~xy\tilde M_{xy} as a quantum mechanical path integral can be assessed. Furthermore, the exact dependence of M~xy\tilde M_{xy} on some geometric scalars can be determined. In two appendices, we discuss boundary effects in the one-dimensional quantum mechanical path integral, and the curved space generalization of the Fock-Schwinger gauge.Comment: 16pp, REVTeX. One additional appendix concerning end-point effects for finite proper-time intervals; inclusion of these effects seem to make our results consistent with those from explicit heat-kernel method

    Black Hole Evaporation in the Presence of a Short Distance Cutoff

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    A derivation of the Hawking effect is given which avoids reference to field modes above some cutoff frequency ωcM1\omega_c\gg M^{-1} in the free-fall frame of the black hole. To avoid reference to arbitrarily high frequencies, it is necessary to impose a boundary condition on the quantum field in a timelike region near the horizon, rather than on a (spacelike) Cauchy surface either outside the horizon or at early times before the horizon forms. Due to the nature of the horizon as an infinite redshift surface, the correct boundary condition at late times outside the horizon cannot be deduced, within the confines of a theory that applies only below the cutoff, from initial conditions prior to the formation of the hole. A boundary condition is formulated which leads to the Hawking effect in a cutoff theory. It is argued that it is possible the boundary condition is {\it not} satisfied, so that the spectrum of black hole radiation may be significantly different from that predicted by Hawking, even without the back-reaction near the horizon becoming of order unity relative to the curvature.Comment: 35 pages, plain LaTeX, UMDGR93-32, NSF-ITP-93-2

    Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

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    We consider a massless scalar field propagating in a weakly curved spacetime whose metric is a solution to the linearized Einstein field equations. The spacetime is assumed to be stationary and asymptotically flat, but no other symmetries are imposed -- the spacetime can rotate and deviate strongly from spherical symmetry. We prove that the late-time behavior of the scalar field is identical to what it would be in a spherically-symmetric spacetime: it decays in time according to an inverse power-law, with a power determined by the angular profile of the initial wave packet (Price falloff theorem). The field's late-time dynamics is insensitive to the nonspherical aspects of the metric, and it is governed entirely by the spacetime's total gravitational mass; other multipole moments, and in particular the spacetime's total angular momentum, do not enter in the description of the field's late-time behavior. This extended formulation of Price's falloff theorem appears to be at odds with previous studies of radiative decay in the spacetime of a Kerr black hole. We show, however, that the contradiction is only apparent, and that it is largely an artifact of the Boyer-Lindquist coordinates adopted in these studies.Comment: 17 pages, RevTeX

    Massive-Field Approach to the Scalar Self Force in Curved Spacetime

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    We derive a new regularization method for the calculation of the (massless) scalar self force in curved spacetime. In this method, the scalar self force is expressed in terms of the difference between two retarded scalar fields: the massless scalar field, and an auxiliary massive scalar field. This field difference combined with a certain limiting process gives the expression for the scalar self-force. This expression provides a new self force calculation method.Comment: 23 pages, few modification

    Improved Effective Potential in Curved Spacetime and Quantum Matter - Higher Derivative Gravity Theory

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    \noindent{\large\bf Abstract.} We develop a general formalism to study the renormalization group (RG) improved effective potential for renormalizable gauge theories ---including matter-R2R^2-gravity--- in curved spacetime. The result is given up to quadratic terms in curvature, and one-loop effective potentials may be easiliy obtained from it. As an example, we consider scalar QED, where dimensional transmutation in curved space and the phase structure of the potential (in particular, curvature-induced phase trnasitions), are discussed. For scalar QED with higher-derivative quantum gravity (QG), we examine the influence of QG on dimensional transmutation and calculate QG corrections to the scalar-to-vector mass ratio. The phase structure of the RG-improved effective potential is also studied in this case, and the values of the induced Newton and cosmological coupling constants at the critical point are estimated. Stability of the running scalar coupling in the Yukawa theory with conformally invariant higher-derivative QG, and in the Standard Model with the same addition, is numerically analyzed. We show that, in these models, QG tends to make the scalar sector less unstable.Comment: 23 pages, Oct 17 199

    Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

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    The presence of fluctuations and non-linear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop {\emph{effective action}} and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop {\emph{finite}} in d=0d=0 and d=1d=1, and is one-loop renormalizable in d=2d=2 and d=3d=3 space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in d=2d=2.Comment: 21 pages, uses ReV-TeX 3.
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