1,723,540 research outputs found
Mathematical structures of space-time
No full textAt first we introduce the space-time manifold and we compare some aspects
of Riemannian and Lorentzian geometry such as the distance function and the
relations between
topology and curvature. We then define spinor structures
in general relativity, and the conditions for their existence are discussed.
The causality conditions are studied through an analysis
of strong causality, stable causality and global hyperbolicity. In looking
at the asymptotic structure of space-time, we focus on the
asymptotic symmetry group of Bondi, Metzner and Sachs, and the b-boundary
construction of Schmidt.
The Hamiltonian structure of space-time
is also analyzed, with emphasis on Ashtekar's spinorial variables.
Finally, the question of a rigorous theory of
singularities in space-times with torsion is addressed, describing in detail
recent work by the author. We define geodesics
as curves whose tangent vector moves by parallel transport. This is different
from what other authors do, because their
definition of geodesics only involves the
Christoffel symbols, though studying theories with torsion.
We then prove how to extend Hawking's singularity
theorem without causality assumptions to the space-time of
the ECSK theory. This is achieved studying the generalized Raychaudhuri
equation in the ECSK theory, the conditions for the existence of
conjugate points and properties of maximal timelike geodesics.
Our result can also be interpreted as a no-singularity theorem if the
torsion tensor does not obey some additional conditions.
Namely, it seems that the occurrence of singularities in closed
cosmological models based on the ECSK theory is less generic than in
general relativity. Our work should be compared with important previous
papers. There
are some relevant differences, because we rely on a different definition of
geodesics, we keep the field equations of the ECSK theory in their original
form rather than casting them in a form similar to general relativity with
a modified energy-momentum tensor, and we emphasize the role played by the
full extrinsic curvature tensor and by the variation formulae
Analysis of unsupported gait in toddlers with autism
No full textAnalysis of unsupported gait in toddlers with autism.
Esposito G, Venuti P, Apicella F, Muratori F.
Department of Cognitive Science and Education, University of Trento, Italy.
[email protected]
AIMS: A number of studies have suggested the importance of motor development in
autism. Motor development has been considered a possible bio-marker of autism
since it does not depend on either social or linguistic development. In this
study, using retrospective video analysis we investigated the first unsupported
gait in toddlers with autism.
METHODS: Fifty-five toddlers, belonging to three groups were recruited: toddlers
with autistic disorder (AD, n=20, age 14.2mo, sd 1.4mo) and as comparison groups:
typically developing toddlers (TD, n=20, age 12.9mo, sd 1.1mo) and toddlers with
non-autistic developmental delays of mixed aetiology (DD, n=15, age 13.1mo, sd
0.8mo). The Walking Observation Scale (WOS) and the Positional Pattern for
Symmetry during Walking (PPSW) were used to gather data on the first unsupported
gait. The WOS includes 11 items that analyze gait through three axes: foot
movements; arm movements; general movements while the PPSW analyses static and
dynamical symmetry during gait.
RESULTS: Our results have identified significant differences in gait patterns
among the group of toddlers with AD as opposed to the control groups. Significant
differences between AD and the two control groups were found for both WOS
(p<.001) and PPSW (p<.001).
CONCLUSION: The specificity of motor disturbances we have identified in autism
(postural asymmetry) is consistent with previous findings that implicated
cerebellar involvement in the motor symptoms of autism
From ordinary to partial differential equations
No full textThis book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value
New photon propagators in quantum electrodynamics
No full textA Lagrangian for quantum electrodynamics is found which makes it explicit that the photon mass is eventually set to zero in the physical part on observational ground. It remains possible to obtain a counterterm Lagrangian where the only non-gauge-invariant term is proportional to the squared divergence of the potential, while the photon propagator in momentum space falls off like k^{−2} at large k, which indeed agrees with perturbative renormalizability. The resulting radiative corrections to the Coulomb potential in QED are also shown to be gauge-independent. A fundamental role of the space of 4-vectors with components given by 4×4 matrices is therefore suggested by our scheme, where such matrices can be used to define a single gauge-averaging functional in the path integral
New application of noncanonical maps in quantum mechanics
No full textOne invertible and one unitary operator can be used to reproduce the effect of a q-deformed
commutator of annihilation and creation operators. The original annihilation
and creation operators are mapped into new operators, not conjugate to each other,
whose standard commutator equals the identity plus a correction proportional to the
original number operator. The consistency condition for the existence of this new set
of operators is derived, by exploiting the Stone theorem on 1-parameter unitary groups.
The above scheme leads to modified “equations of motion” which do not preserve the
properties of the original first-order set for annihilation and creation operators. Their
relation with commutation relations is also studied
Local supersymmetry in one-loop quantum cosmology
No full textThe contribution of physical degrees of freedom to
the one-loop amplitudes of Euclidean supergravity is here evaluated
in the case of flat Euclidean backgrounds bounded by a three-sphere,
recently considered in perturbative quantum cosmology.
In Euclidean supergravity, the spin-3/2
potential has the pair of independent spatial components
(psi_{i}^{A}, {widetilde psi}_{i}^{A'}).
Massless gravitinos are here
subject to the following local boundary conditions
on S**3: sqrt{2} ; {_{e}n_{A}^{; ; A'}}
psi_{i}^{A}=pm {widetilde psi}_{i}^{A'},
where {_{e}n_{A}^{; ; A'}} is the Euclidean
normal to the three-sphere boundary.
The physical degrees of freedom (denoted by PDF)
are picked out imposing the supersymmetry
constraints and choosing the gauge condition
e_{AA'}^{; ; ; ; ; i}psi_{i}^{A}=0,
e_{AA'}^{; ; ; ; ; i}{widetilde psi}_{i}^{A'}=0.
These local boundary conditions are then
found to imply the eigenvalue condition
{[J_{n+2}(E)]}^{2}-{[J_{n+3}(E)]}^{2}=0,
; forall n geq 0, with degeneracy
(n+4)(n+1). One can thus apply again a
zeta-function technique previously
used for massless spin- fields.
The PDF contribution to the full zeta(0) value is found to be
=-289/360. Remarkably, for the
massless gravitino field the PDF method and
local boundary conditions lead to
a result for zeta(0) which is equal to the PDF value one obtains
using spectral boundary conditions on S**3
Nonlocal boundary conditions in Euclidean quantum gravity
No full textNon-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; in 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 4-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
Mazzurega, M., Occelli, V., Garberi, P., Esposito, G., & Zampini, M. (2014). Body representation and interpersonal socio affective factors: The enfacement illusion modulated by autistic-like traits. International Multisensory Research Forum, Amsterdam, The Netherlands, June, 11-14.
No full textAsymptotic heat kernels in quantum field theory
No full textAsymptotic expansions were first introduced by Henri Poincar ́e in 1886. This paper describes their application to the semi-classical evaluation of amplitudes in quantum field theory with boundaries. By using zeta-function regularization, the conformal anomaly for a massless spin-1/2 field in flat Euclidean backgrounds with boundary is obtained on imposing locally supersymmetric boundary conditions. The quantization program for gauge fields and gravitation in the presence of boundaries is then introduced by focusing on conformal anomalies for higher-spin fields. The conditions under which the covariant Schwinger-DeWitt and the non-covariant, mode-by-mode analysis of quantum amplitudes agree are described
Gauge-averaging functionals for Euclidean Maxwell theory in the presence of boundaries
No full textThis paper studies the one-loop expansion of the amplitudes of electromagnetism
about flat Euclidean backgrounds bounded by a 3-sphere, recently considered in perturbative
quantum cosmology, by using zeta-function regularization. For a specific choice of gauge averaging
functional, the contributions to the full zeta(0) value owed to physical degrees offreedom,
decoupled gauge mode, coupled gauge modes, and Paddeev-Popov ghost field are derived in
detail, and alternative choices for such a functional are also studied. This analysis enables one
to get a better understanding of different quantization techniques for gauge fields and gravitation
in the presence of boundarie
- …
