102 research outputs found
Late Holocene relative sea levels near Palmer Station, northern Antarctic Peninsula, strongly controlled by late Holocene ice-mass changes
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
We study the renormalization of the nonlinear effective SU(2) Lagrangian up
to 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
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
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
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, in
powers of can be made in a number of ways. For (the case of interest
when doing one-loop calculations) numerous approaches have been employed to
determine this expansion to very high order; when (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 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 as a quantum mechanical path integral can be assessed. Furthermore, the
exact dependence of 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
A derivation of the Hawking effect is given which avoids reference to field
modes above some cutoff frequency 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
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
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
\noindent{\large\bf Abstract.} We develop a general formalism to study the
renormalization group (RG) improved effective potential for renormalizable
gauge theories ---including matter--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
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 and
, and is one-loop renormalizable in and space dimensions. We
obtain the one-loop renormalization group equations and find they run with
scale only in .Comment: 21 pages, uses ReV-TeX 3.
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