14,733 research outputs found
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
Spin-Raising Operators and Spin-3/2 Potentials in Quantum Cosmology
Local boundary conditions involving field strengths and the normal to the
boundary, originally studied in anti-de Sitter space-time, have been recently
considered in one-loop quantum cosmology. This paper derives the conditions
under which spin-raising operators preserve these local boundary conditions on
a 3-sphere for fields of spin 0,1/2,1,3/2 and 2. Moreover, the two-component
spinor analysis of the four potentials of the totally symmetric and independent
field strengths for spin 3/2 is applied to the case of a 3-sphere boundary. It
is shown that such boundary conditions can only be imposed in a flat Euclidean
background, for which the gauge freedom in the choice of the potentials
remains.Comment: 13 pages, plain-tex, recently appearing in Classical and Quantum
Gravity, volume 11, April 1994, pages 897-903. Apologies for the delay in
circulating the file, due to technical problems now fixe
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
The first deep X-ray and optical observations of the closest isolated radio pulsar
With a distance of 170 pc, PSR J2144-3933 is the closest isolated radio
pulsar currently known. It is also the slowest and least energetic radio
pulsar; indeed, its radio emission is difficult to account for with standard
pulsar models, since its position in the P-Pdot diagram is far beyond typical
"death lines". Here we present the first deep X-ray and optical observations of
PSR J2144-3933, performed in 2009 with XMM-Newton and the VLT, from which we
can set one of the most robust upper limits on the surface temperature of a
neutron star. We have also explored the possibility of measuring the neutron
star mass from the gravitational lensing effect on a background optical source.Comment: 4 pages, 3 figures; to appear in the Proceedings of the Pulsar
Conference 2010, Chia, Sardinia (Italy), 10-15 October 201
On the 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, and on the ghost fields. The
scheme requires that temporal and tangential components of perturbations of the
potential should vanish at the boundary, jointly with the gauge-averaging
functional, first chosen of the Lorenz 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 the potential, jointly with the decoupled normal mode of the
potential. Moreover, normal and longitudinal components of the potential 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 non-covariant gauges.Comment: 29 pages, Revtex, revised version. In this last version, a new
section has been added, devoted to the zero-point energy of a conducting
spherical shell in the axial gauge. A second appendix has also been include
A New Family of Gauges in Linearized General Relativity
For vacuum Maxwell theory in four dimensions, a supplementary condition
exists (due to Eastwood and Singer) which is invariant under conformal
rescalings of the metric, in agreement with the conformal symmetry of the
Maxwell equations. Thus, starting from the de Donder gauge, which is not
conformally invariant but is the gravitational counterpart of the Lorenz gauge,
one can consider, led by formal analogy, a new family of gauges in general
relativity, which involve fifth-order covariant derivatives of metric
perturbations. The admissibility of such gauges in the classical theory is
first proven in the cases of linearized theory about flat Euclidean space or
flat Minkowski space-time. In the former, the general solution of the equation
for the fulfillment of the gauge condition after infinitesimal diffeomorphisms
involves a 3-harmonic 1-form and an inverse Fourier transform. In the latter,
one needs instead the kernel of powers of the wave operator, and a contour
integral. The analysis is also used to put restrictions on the dimensionless
parameter occurring in the DeWitt supermetric, while the proof of admissibility
is generalized to a suitable class of curved Riemannian backgrounds.
Eventually, a non-local construction is obtained of the tensor field which
makes it possible to achieve conformal invariance of the above gauges.Comment: 28 pages, plain Tex. In the revised version, sections 4 and 5 are
completely ne
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