8,491 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
Flavour-conserving oscillations of Dirac-Majorana neutrinos
We analyze both chirality-changing and chirality-preserving transitions of
Dirac-Majorana neutrinos. In vacuum, the first ones are suppressed with respect
to the others due to helicity conservation and the interactions with a
(``normal'') medium practically does not affect the expressions of the
probabilities for these transitions, even if the amplitudes of oscillations
slightly change. For usual situations involving relativistic neutrinos we find
no resonant enhancement for all flavour-conserving transitions. However, for
very light neutrinos propagating in superdense media, the pattern of
oscillations is dramatically altered with respect to the
vacuum case, the transition probability practically vanishing. An application
of this result is envisaged.Comment: 14 pages, latex 2E, no figure
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
Radiometric infrared focal plane array imaging system for thermographic applications
This document describes research performed under the Radiometric Infrared Focal Plane Array Imaging System for Thermographic Applications contract. This research investigated the feasibility of using platinum silicide (PtSi) Schottky-barrier infrared focal plane arrays (IR FPAs) for NASA Langley's specific radiometric thermal imaging requirements. The initial goal of this design was to develop a high spatial resolution radiometer with an NETD of 1 percent of the temperature reading over the range of 0 to 250 C. The proposed camera design developed during this study and described in this report provides: (1) high spatial resolution (full-TV resolution); (2) high thermal dynamic range (0 to 250 C); (3) the ability to image rapid, large thermal transients utilizing electronic exposure control (commandable dynamic range of 2,500,000:1 with exposure control latency of 33 ms); (4) high uniformity (0.5 percent nonuniformity after correction); and (5) high thermal resolution (0.1 C at 25 C background and 0.5 C at 250 C background)
The critical dimension for a 4th order problem with singular nonlinearity
We study the regularity of the extremal solution of the semilinear biharmonic
equation \bi u=\f{\lambda}{(1-u)^2}, which models a simple
Micro-Electromechanical System (MEMS) device on a ball B\subset\IR^N, under
Dirichlet boundary conditions on . We complete
here the results of F.H. Lin and Y.S. Yang \cite{LY} regarding the
identification of a "pull-in voltage" \la^*>0 such that a stable classical
solution u_\la with 0 exists for \la\in (0,\la^*), while there is
none of any kind when \la>\la^*. Our main result asserts that the extremal
solution is regular provided while is singular () for , in which case
on the unit ball, where
and .Comment: 19 pages. This paper completes and replaces a paper (with a similar
title) which appeared in arXiv:0810.5380. Updated versions --if any-- of this
author's papers can be downloaded at this http://www.birs.ca/~nassif
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
Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions
A general method is known to exist for studying Abelian and non-Abelian gauge
theories, as well as Euclidean quantum gravity, at one-loop level on manifolds
with boundary. In the latter case, boundary conditions on metric perturbations
h can be chosen to be completely invariant under infinitesimal diffeomorphisms,
to preserve the invariance group of the theory and BRST symmetry. In the de
Donder gauge, however, the resulting boundary-value problem for the Laplace
type operator acting on h is known to be self-adjoint but not strongly
elliptic. The latter is a technical condition ensuring that a unique smooth
solution of the boundary-value problem exists, which implies, in turn, that the
global heat-kernel asymptotics yielding one-loop divergences and one-loop
effective action actually exists. The present paper shows that, on the
Euclidean four-ball, only the scalar part of perturbative modes for quantum
gravity are affected by the lack of strong ellipticity. Further evidence for
lack of strong ellipticity, from an analytic point of view, is therefore
obtained. Interestingly, three sectors of the scalar-perturbation problem
remain elliptic, while lack of strong ellipticity is confined to the remaining
fourth sector. The integral representation of the resulting zeta-function
asymptotics is also obtained; this remains regular at the origin by virtue of a
spectral identity here obtained for the first time.Comment: 25 pages, Revtex-4. Misprints in Eqs. (5.11), (5.14), (5.16) have
been correcte
One-Loop Divergences in Simple Supergravity: Boundary Effects
This paper studies the semiclassical approximation of simple supergravity in
Riemannian four-manifolds with boundary, within the framework of
-function regularization. The massless nature of gravitinos, jointly
with the presence of a boundary and a local description in terms of potentials
for spin , force the background to be totally flat. First, nonlocal
boundary conditions of the spectral type are imposed on spin-
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 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
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.Comment: 37 pages, Revtex. Equations (5.2), (5.3), (5.5), (5.7), (5.8) and
(5.13) have been amended, jointly with a few misprint
Lack of strong ellipticity in Euclidean quantum gravity
Recent work in Euclidean quantum gravity has studied boundary conditions
which are completely invariant under infinitesimal diffeomorphisms on metric
perturbations. On using the de Donder gauge-averaging functional, this scheme
leads to both normal and tangential derivatives in the boundary conditions. In
the present paper, it is proved that the corresponding boundary value problem
fails to be strongly elliptic. The result raises deep interpretative issues for
Euclidean quantum gravity on manifolds with boundary.Comment: 14 pages, Plain Tex, 33 KB, no figure
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