12,759 research outputs found
Linear Form of Canonical Gravity
Recent work in the literature has shown that general relativity can be
formulated in terms of a jet bundle which, in local coordinates, has five
entries: local coordinates on Lorentzian space-time, tetrads, connection
one-forms, multivelocities corresponding to the tetrads and multivelocities
corresponding to the connection one-forms. The derivatives of the Lagrangian
with respect to the latter class of multivelocities give rise to a set of
multimomenta which naturally occur in the constraint equations. Interestingly,
all the constraint equations of general relativity are linear in terms of this
class of multimomenta. This construction has been then extended to complex
general relativity, where Lorentzian space-time is replaced by a
four-complex-dimensional complex-Riemannian manifold. One then finds a
holomorphic theory where the familiar constraint equations are replaced by a
set of equations linear in the holomorphic multimomenta, providing such
multimomenta vanish on a family of two-complex-dimensional surfaces. In quantum
gravity, the problem arises to quantize a real or a holomorphic theory on the
extended space where the multimomenta can be defined.Comment: 5 pages, plain-te
Essential self-adjointness in one-loop quantum cosmology
The quantization of closed cosmologies makes it necessary to study squared
Dirac operators on closed intervals and the corresponding quantum amplitudes.
This paper proves self-adjointness of these second-order elliptic operators.Comment: 14 pages, plain Tex. An Erratum has been added to the end, which
corrects section
Singularity Theory in Classical Cosmology
This paper compares recent approaches appearing in the literature on the
singularity problem for space-times with nonvanishing torsion.Comment: 4 pages, plain-tex, published in Nuovo Cimento B, volume 107, pages
849-851, year 199
One-Loop Effective Action for Euclidean Maxwell Theory on Manifolds with 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 Faddeev-Popov formalism and
-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
or 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.Comment: 25 pages, Revte
New Developments in the Spectral Asymptotics of Quantum Gravity
A vanishing one-loop wave function of the Universe in the limit of small
three-geometry is found, on imposing diffeomorphism-invariant boundary
conditions on the Euclidean 4-ball in the de Donder gauge. This result suggests
a quantum avoidance of the cosmological singularity driven by full
diffeomorphism invariance of the boundary-value problem for one-loop quantum
theory. All of this is made possible by a peculiar spectral cancellation on the
Euclidean 4-ball, here derived and discussed.Comment: 7 pages, latex file. Paper prepared for the Conference "QFEXT05:
Quantum Field Theory Under the Influence of External Conditions", Barcelona,
September 5 - September 9, 2005. In the final version, the presentation has
been further improved, and yet other References have been adde
Kinetics of a Model Weakly Ionized Plasma in the Presence of Multiple Equilibria
We study, globaly in time, the velocity distribution of a spatially
homogeneous system that models a system of electrons in a weakly ionized
plasma, subjected to a constant external electric field . The density
satisfies a Boltzmann type kinetic equation containing a full nonlinear
electron-electron collision term as well as linear terms representing
collisions with reservoir particles having a specified Maxwellian distribution.
We show that when the constant in front of the nonlinear collision kernel,
thought of as a scaling parameter, is sufficiently strong, then the
distance between and a certain time dependent Maxwellian stays small
uniformly in . Moreover, the mean and variance of this time dependent
Maxwellian satisfy a coupled set of nonlinear ODE's that constitute the
``hydrodynamical'' equations for this kinetic system. This remain true even
when these ODE's have non-unique equilibria, thus proving the existence of
multiple stabe stationary solutions for the full kinetic model. Our approach
relies on scale independent estimates for the kinetic equation, and entropy
production estimates. The novel aspects of this approach may be useful in other
problems concerning the relation between the kinetic and hydrodynamic scales
globably in time.Comment: 30 pages, in TeX, to appear in Archive for Rational Mechanics and
Analysis: author's email addresses: [email protected],
[email protected], [email protected],
[email protected], [email protected]
Propagation of Chaos for a Thermostated Kinetic Model
We consider a system of N point particles moving on a d-dimensional torus.
Each particle is subject to a uniform field E and random speed conserving
collisions. This model is a variant of the Drude-Lorentz model of electrical
conduction. In order to avoid heating by the external field, the particles also
interact with a Gaussian thermostat which keeps the total kinetic energy of the
system constant. The thermostat induces a mean-field type of interaction
between the particles. Here we prove that, starting from a product measure, in
the large N limit, the one particle velocity distribution satisfies a self
consistent Vlasov-Boltzmann equation.. This is a consequence of "propagation of
chaos", which we also prove for this model.Comment: This version adds affiliation and grant information; otherwise it is
unchange
A Suzaku X-ray observation of one orbit of the supergiant fast X-ray transient IGR J16479-4514
We report on a 250 ks long X-ray observation of the supergiant fast X-ray
transient (SFXT) IGR J16479-4514 performed with Suzaku in 2012 February. About
80% of the short orbital period (Porb=3.32 days) was covered as continuously as
possible for the first time. The source light curve displays variability of
more than two orders of magnitude, starting with a very low emission state
lasting the first 46 ks (1E-13 erg/cm2/s, 1-10 keV), consistent with being due
to the X-ray eclipse by the supergiant companion. The transition to the
uneclipsed X-ray emission is energy dependent. Outside the eclipse, the source
spends most of the time at a level of (6-7)x10^-12 erg/cm2/s punctuated by two
structured faint flares with a duration of about 10 and 15 ks. Remarkably, the
first faint flare occurs at a similar orbital phase of the bright flares
previously observed in the system. This indicates the presence of a
phase-locked large scale structure in the supergiant wind, driving a higher
accretion rate onto the compact object. The scattered component visible during
the X-ray eclipse allowed us to directly probe the wind density at the orbital
separation, resulting in rho=7E-14 g/cm3. Assuming a spherical geometry for the
supergiant wind, the derived wind density translates into a ratio
Mdot_w/v_terminal = 7E-17 solar masses/km which, assuming terminal velocities
in a large range 500-3000 km/s, implies an accretion luminosity two orders of
magnitude higher than that observed. As a consequence, a mechanism is at work
reducing the mass accretion rate. Different possibilities are discussed.Comment: Accepted for publication in MNRAS. 10 pages, 5 figure
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