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Some Implications of the Cosmological Constant to Fundamental Physics
In the presence of a cosmological constant, ordinary Poincare' special
relativity is no longer valid and must be replaced by a de Sitter special
relativity, in which Minkowski space is replaced by a de Sitter spacetime. In
consequence, the ordinary notions of energy and momentum change, and will
satisfy a different kinematic relation. Such a theory is a different kind of a
doubly special relativity. Since the only difference between the Poincare' and
the de Sitter groups is the replacement of translations by certain linear
combinations of translations and proper conformal transformations, the net
result of this change is ultimately the breakdown of ordinary translational
invariance. From the experimental point of view, therefore, a de Sitter special
relativity might be probed by looking for possible violations of translational
invariance. If we assume the existence of a connection between the energy scale
of an experiment and the local value of the cosmological constant, there would
be changes in the kinematics of massive particles which could hopefully be
detected in high-energy experiments. Furthermore, due to the presence of a
horizon, the usual causal structure of spacetime would be significantly
modified at the Planck scale.Comment: 15 pages, lecture presented at the "XIIth Brazilian School of
Cosmology and Gravitation", Mangaratiba, Rio de Janeiro, September 10-23,
200
Cosmological Term and Fundamental Physics
A nonvanishing cosmological term in Einstein's equations implies a
nonvanishing spacetime curvature even in absence of any kind of matter. It
would, in consequence, affect many of the underlying kinematic tenets of
physical theory. The usual commutative spacetime translations of the Poincare'
group would be replaced by the mixed conformal translations of the de Sitter
group, leading to obvious alterations in elementary concepts such as time,
energy and momentum. Although negligible at small scales, such modifications
may come to have important consequences both in the large and for the
inflationary picture of the early Universe. A qualitative discussion is
presented which suggests deep changes in Hamiltonian, Quantum and Statistical
Mechanics. In the primeval universe as described by the standard cosmological
model, in particular, the equations of state of the matter sources could be
quite different from those usually introduced.Comment: RevTeX, 4 pages. Selected for Honorable Mention in the Annual Essay
Competition of the Gravity Research Foundation for the year 200
Gravitation as Anholonomy
A gravitational field can be seen as the anholonomy of the tetrad fields.
This is more explicit in the teleparallel approach, in which the gravitational
field-strength is the torsion of the ensuing Weitzenboeck connection. In a
tetrad frame, that torsion is just the anholonomy of that frame. The infinitely
many tetrad fields taking the Lorentz metric into a given Riemannian metric
differ by point-dependent Lorentz transformations. Inertial frames constitute a
smaller infinity of them, differing by fixed-point Lorentz transformations.
Holonomic tetrads take the Lorentz metric into itself, and correspond to
Minkowski flat spacetime. An accelerated frame is necessarily anholonomic and
sees the electromagnetic field strength with an additional term.Comment: RevTeX4, 10 pages, no figures. To appear in Gen. Rel. Gra
The Equivalence Principle Revisited
A precise formulation of the strong Equivalence Principle is essential to the
understanding of the relationship between gravitation and quantum mechanics.
The relevant aspects are reviewed in a context including General Relativity,
but allowing for the presence of torsion. For the sake of brevity, a concise
statement is proposed for the Principle: "An ideal observer immersed in a
gravitational field can choose a reference frame in which gravitation goes
unnoticed". This statement is given a clear mathematical meaning through an
accurate discussion of its terms. It holds for ideal observers (time-like
smooth non-intersecting curves), but not for real, spatially extended
observers. Analogous results hold for gauge fields. The difference between
gravitation and the other fundamental interactions comes from their distinct
roles in the equation of force.Comment: RevTeX, 18 pages, no figures, to appear in Foundations of Physic
The whole mesh Deformation Model for 2D and 3D image segmentation
In this paper we present a novel approach for image segmentation using Active Nets and Active Volumes. Those solutions are based on the Deformable Models, with slight difference in the method for describing the shapes of interests - instead of using a contour or a surface they represented the segmented objects with a mesh structure, which allows to describe not only the surface of the objects but also to model their interiors. This is obtained by dividing the nodes of the mesh in two categories, namely internal and external ones, which will be responsible for two different tasks. In our new approach we propose to negate this separation and use only one type of nodes. Using that assumption we manage to significantly shorten the time of segmentation while maintaining its quality
Tunable quantum dots in bilayer graphene
We demonstrate theoretically that quantum dots in bilayers of graphene can be
realized. A position-dependent doping breaks the equivalence between the upper
and lower layer and lifts the degeneracy of the positive and negative momentum
states of the dot. Numerical results show the simultaneous presence of electron
and hole confined states for certain doping profiles and a remarkable angular
momentum dependence of the quantum dot spectrum which is in sharp contrast with
that for conventional semiconductor quantum dots. We predict that the optical
spectrum will consist of a series of non-equidistant peaks.Comment: 5 pages, to appear in Nano Letter
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