11,439 research outputs found
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
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
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
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
Relativistic Gauge Conditions in Quantum Cosmology
This paper studies the quantization of the electromagnetic field on a flat
Euclidean background with boundaries. One-loop scaling factors are evaluated
for the one-boundary and two-boundary backgrounds. The mode-by-mode analysis of
Faddeev-Popov quantum amplitudes is performed by using zeta-function
regularization, and is compared with the space-time covariant evaluation of the
same amplitudes. It is shown that a particular gauge condition exists for which
the corresponding operator matrix acting on gauge modes is in diagonal form
from the beginning. Moreover, various relativistic gauge conditions are studied
in detail, to investigate the gauge invariance of the perturbative quantum
theory.Comment: 26 pages, plain TeX, no figure
A Non-Singular One-Loop Wave Function of the Universe From a New Eigenvalue Asymptotics in Quantum Gravity
Recent work on Euclidean quantum gravity on the four-ball has proved
regularity at the origin of the generalized zeta-function built from
eigenvalues for metric and ghost modes, when diffeomorphism-invariant boundary
conditions are imposed in the de Donder gauge. The hardest part of the analysis
involves one of the four sectors for scalar-type perturbations, the eigenvalues
of which are obtained by squaring up roots of a linear combination of Bessel
functions of integer adjacent orders, with a coefficient of linear combination
depending on the unknown roots. This paper obtains, first, approximate analytic
formulae for such roots for all values of the order of Bessel functions. For
this purpose, both the descending series for Bessel functions and their uniform
asymptotic expansion at large order are used. The resulting generalized
zeta-function is also built, and another check of regularity at the origin is
obtained. For the first time in the literature on quantum gravity on manifolds
with boundary, a vanishing one-loop wave function of the Universe is found in
the limit of small three-geometry, which suggests a quantum avoidance of the
cosmological singularity driven by full diffeomorphism invariance of the
boundary-value problem for one-loop quantum theory.Comment: 21 Pages, Latex and .eps files with JHEP3 style. The discussion in
Section 5 has been improved, and Ref. 26 has been adde
Stochastically driven single level quantum dot: a nano-scale finite-time thermodynamic machine and its various operational modes
We describe a single-level quantum dot in contact with two leads as a
nanoscale finite-time thermodynamic machine. The dot is driven by an external
stochastic force that switches its energy between two values. In the isothermal
regime, it can operate as a rechargeable battery by generating an electric
current against the applied bias in response to the stochastic driving, and
re-delivering work in the reverse cycle. This behavior is reminiscent of the
Parrondo paradox. If there is a thermal gradient the device can function as a
work-generating thermal engine, or as a refrigerator that extracts heat from
the cold reservoir via the work input of the stochastic driving. The efficiency
of the machine at maximum power output is investigated for each mode of
operation, and universal features are identified.Comment: 4 pages, 3 figures, V2: typos corrected around eq.(12
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
One-Loop Amplitudes in Euclidean Quantum Gravity
This paper studies the linearized gravitational field in the presence of
boundaries. For this purpose, -function regularization is used to
perform the mode-by-mode evaluation of BRST-invariant Faddeev-Popov amplitudes
in the case of flat Euclidean four-space bounded by a three-sphere. On choosing
the de Donder gauge-averaging term, the resulting value is found to
agree with the space-time covariant calculation of the same amplitudes, which
relies on the recently corrected geometric formulas for the asymptotic heat
kernel in the case of mixed boundary conditions. Two sets of mixed boundary
conditions for Euclidean quantum gravity are then compared in detail. The
analysis proves that one cannot restrict the path-integral measure to
transverse-traceless perturbations. By contrast, gauge-invariant amplitudes are
only obtained on considering from the beginning all perturbative modes of the
gravitational field, jointly with ghost modes.Comment: 26 pages, plain TeX, no figure
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