21,627 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

### 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

### Quantized Maxwell Theory in a Conformally Invariant Gauge

Maxwell theory can be studied in a gauge which is invariant under conformal
rescalings of the metric, and first proposed by Eastwood and Singer. This paper
studies the corresponding quantization in flat Euclidean 4-space. The resulting
ghost operator is a fourth-order elliptic operator, while the operator P on
perturbations of the potential is a sixth-order elliptic operator. The operator
P may be reduced to a second-order non-minimal operator if a dimensionless
gauge parameter tends to infinity. Gauge-invariant boundary conditions are
obtained by setting to zero at the boundary the whole set of perturbations of
the potential, jointly with ghost perturbations and their normal derivative.
This is made possible by the fourth-order nature of the ghost operator. An
analytic representation of the ghost basis functions is also obtained.Comment: 8 pages, plain Tex. In this revised version, the calculation of ghost
basis functions has been amended, and the presentation has been improve

### 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

### Alpha Surfaces for Complex Space-Times with Torsion

This paper studies necessary conditions for the existence of alpha-surfaces
in complex space-time manifolds with nonvanishing torsion. For these manifolds,
Lie brackets of vector fields and spinor Ricci identities contain explicitly
the effects of torsion. This leads to an integrability condition for
alpha-surfaces which does not involve just the self-dual Weyl spinor, as in
complex general relativity, but also the torsion spinor, in a nonlinear way,
and its covariant derivative. Interestingly, a particular solution of the
integrability condition is given by conformally right-flat and
right-torsion-free space-times.Comment: 7 pages, plain-tex, published in Nuovo Cimento B, volume 108, pages
123-125, year 199

### 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

### Generalized Ginzburg-Landau models for non-conventional superconductors

We review some recent extensions of the Ginzburg-Landau model able to
describe several properties of non-conventional superconductors. In the first
extension, s-wave superconductors endowed with two different critical
temperatures are considered, their main thermodynamical and magnetic properties
being calculated and discussed. Instead in the second extension we describe
spin-triplet superconductivity (with a single critical temperature), studying
in detail the main predicted physical properties. A thorough discussion of the
peculiar predictions of our models and their physical consequences is as well
performed.Comment: 16 pages, 2 figure

### 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

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