9,393 research outputs found
Non-Local Boundary Conditions in Euclidean Quantum Gravity
Non-local boundary conditions for Euclidean quantum gravity are proposed,
consisting of an integro-differential boundary operator acting on metric
perturbations. In this case, the operator P on metric perturbations is of
Laplace type, subject to non-local boundary conditions; by contrast, its
adjoint is the sum of a Laplacian and of a singular Green operator, subject to
local boundary conditions. Self-adjointness of the boundary-value problem is
correctly formulated by looking at Dirichlet-type and Neumann-type realizations
of the operator P, following recent results in the literature. The set of
non-local boundary conditions for perturbative modes of the gravitational field
is written in general form on the Euclidean four-ball. For a particular choice
of the non-local boundary operator, explicit formulae for the boundary-value
problem are obtained in terms of a finite number of unknown functions, but
subject to some consistency conditions. Among the related issues, the problem
arises of whether non-local symmetries exist in Euclidean quantum gravity.Comment: 23 pages, plain Tex. The revised version is much longer, and new
original calculations are presented in section
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
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
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
Energy Deposition Studies for the Hi-Lumi LHC Inner Triplet Magnets
A detailed model of the High Luminosity LHC inner triplet region with new
large-aperture Nb3Sn magnets, field maps, corrector packages, and segmented
tungsten inner absorbers was built and implemented into the FLUKA and MARS15
codes. In the optimized configuration, the peak power density averaged over the
magnet inner cable width is safely below the quench limit. For the integrated
luminosity of 3000 fb -1, the peak dose in the innermost magnet insulator
ranges from 20 to 35 MGy. Dynamic heat loads to the triplet magnet cold mass
are calculated to evaluate the cryogenic capability. In general, FLUKA and MARS
results are in a very good agreement.Comment: 4 pp. Presented paper at the 5th International Particle Accelerator
Conference, June 15 -20, 2014, Dresden, German
Rarita-Schwinger Potentials in Quantum Cosmology
This paper studies the two-spinor form of the Rarita-Schwinger potentials
subject to local boundary conditions compatible with local supersymmetry. The
massless Rarita-Schwinger field equations are studied in four-real-dimensional
Riemannian backgrounds with boundary. Gauge transformations on the potentials
are shown to be compatible with the field equations providing the background is
Ricci-flat, in agreement with previous results in the literature. However, the
preservation of boundary conditions under such gauge transformations leads to a
restriction of the gauge freedom. The recent construction by Penrose of
secondary potentials which supplement the Rarita-Schwinger potentials is then
applied. The equations for the secondary potentials, jointly with the boundary
conditions, imply that the background four-geometry is further restricted to be
totally flat.Comment: 23 pages, plain TeX, no figures. The paper has been completely
revise
Energy deposition studies for the High-Luminosity Large Hadron Collider inner triplet magnets
A detailed model of the High Luminosity LHC inner triplet region with new
large-aperture Nb3Sn magnets, field maps, corrector packages, and segmented
tungsten inner absorbers was built and implemented into the FLUKA and MARS15
codes. In the optimized configuration, the peak power density averaged over the
magnet inner cable width is safely below the quench limit. For the integrated
luminosity of 3000 fb-1, the peak dose in the innermost magnet insulator ranges
from 20 to 35 MGy. Dynamic heat loads to the triplet magnet cold mass are
calculated to evaluate the cryogenic capability. In general, FLUKA and MARS
results are in a very good agreement.Comment: 24 p
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
New Kernels in Quantum Gravity
Recent work in the literature has proposed the use of non-local boundary
conditions in Euclidean quantum gravity. The present paper studies first a more
general form of such a scheme for bosonic gauge theories, by adding to the
boundary operator for mixed boundary conditions of local nature a two-by-two
matrix of pseudo-differential operators with pseudo-homogeneous kernels. The
request of invariance of such boundary conditions under infinitesimal gauge
transformations leads to non-local boundary conditions on ghost fields. In
Euclidean quantum gravity, an alternative scheme is proposed, where non-local
boundary conditions and the request of their complete gauge invariance are
sufficient to lead to gauge-field and ghost operators of pseudo-differential
nature. The resulting boundary conditions have a Dirichlet and a
pseudo-differential sector, and are pure Dirichlet for the ghost. This approach
is eventually extended to Euclidean Maxwell theory.Comment: 19 pages, plain Tex. In this revised version, section 5 is new,
section 3 is longer, and the presentation has been improve
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