481 research outputs found
de Sitter relativity: a natural scenario for an evolving Lambda
The dispersion relation of de Sitter special relativity is obtained in a
simple and compact form, which is formally similar to the dispersion relation
of ordinary special relativity. It is manifestly invariant under change of
scale of mass, energy and momentum, and can thus be applied at any energy
scale. When applied to the universe as a whole, the de Sitter special
relativity is found to provide a natural scenario for the existence of an
evolving cosmological term, and agrees in particular with the present-day
observed value. It is furthermore consistent with a conformal cyclic view of
the universe, in which the transition between two consecutive eras occurs
through a conformal invariant spacetime.Comment: V1: 11 pages. V2: Presentation changes, new discussion added, 13
page
de Sitter geodesics: reappraising the notion of motion
The de Sitter spacetime is transitive under a combination of translations and
proper conformal transformations. Its usual family of geodesics, however, does
not take into account this property. As a consequence, there are points in de
Sitter spacetime which cannot be joined to each other by any one of these
geodesics. By taking into account the appropriate transitivity properties in
the variational principle, a new family of maximizing trajectories is obtained,
whose members are able to connect any two points of the de Sitter spacetime.
These geodesics introduce a new notion of motion, given by a combination of
translations and proper conformal transformations, which may possibly become
important at very-high energies, where conformal symmetry plays a significant
role.Comment: 9 pages. V2: Presentation changes aiming at clarifying the text;
version accepted for publication in Gen. Rel. Gra
Gravitomagnetic Moments of the Fundamental Fields
The quadratic form of the Dirac equation in a Riemann spacetime yields a
gravitational gyromagnetic ratio \kappa_S = 2 for the interaction of a Dirac
spinor with curvature. A gravitational gyromagnetic ratio \kappa_S = 1 is also
found for the interaction of a vector field with curvature. It is shown that
the Dirac equation in a curved background can be obtained as the square--root
of the corresponding vector field equation only if the gravitational
gyromagnetic ratios are properly taken into account.Comment: 8 pages, RevTeX Style, no figures, changed presentation -- now
restricted to fields of spin 0, 1/2 and 1 -- some references adde
Bringing Together Gravity and the Quanta
Due to its underlying gauge structure, teleparallel gravity achieves a
separation between inertial and gravitational effects. It can, in consequence,
describe the isolated gravitational interaction without resorting to the
equivalence principle, and is able to provide a tensorial definition for the
energy-momentum density of the gravitational field. Considering the conceptual
conflict between the local equivalence principle and the nonlocal uncertainty
principle, the replacement of general relativity by its teleparallel equivalent
can be considered an important step towards a prospective reconciliation
between gravitation and quantum mechanics.Comment: 9 pages. Contribution to the proceedings of the Albert Einstein
Century International Conference, Paris, 18-22 July, 200
Mass Generation from Lie Algebra Extensions
Applied to the electroweak interactions, the theory of Lie algebra extensions
suggests a mechanism by which the boson masses are generated without resource
to spontaneous symmetry breaking. It starts from a gauge theory without any
additional scalar field. All the couplings predicted by the Weinberg-Salam
theory are present, and a few others which are nevertheless consistent within
the model.Comment: 11 pages; revtex; title and PACS have been changed; comments included
in the manuscrip
Toda Fields on Riemann Surfaces: remarks on the Miura transformation
We point out that the Miura transformation is related to a holomorphic
foliation in a relative flag manifold over a Riemann Surface. Certain
differential operators corresponding to a free field description of
--algebras are thus interpreted as partial connections associated to the
foliation.Comment: AmsLatex 1.1, 10 page
Extensions of Picard 2-Stacks and the cohomology groups Ext^i of length 3 complexes
The aim of this paper is to define and study the 3-category of extensions of
Picard 2-stacks over a site S and to furnish a geometrical description of the
cohomology groups Ext^i of length 3 complexes of abelian sheaves. More
precisely, our main Theorem furnishes
(1) a parametrization of the equivalence classes of objects, 1-arrows,
2-arrows, and 3-arrows of the 3-category of extensions of Picard 2-stacks by
the cohomology groups Ext^i, and
(2) a geometrical description of the cohomology groups Ext^i of length 3
complexes of abelian sheaves via extensions of Picard 2-stacks.
To this end, we use the triequivalence between the 3-category of Picard
2-stacks and the tricategory T^[-2,0](S) of length 3 complexes of abelian
sheaves over S introduced by the second author in arXiv:0906.2393, and we
define the notion of extension in this tricategory T^[-2,0](S), getting a pure
algebraic analogue of the 3-category of extensions of Picard 2-stacks. The
calculus of fractions that we use to define extensions in the tricategory
T^[-2,0](S) plays a central role in the proof of our Main Theorem.Comment: 2 New Appendix: in the first Appendix we compute a long exact
sequence involving the homotopy groups of an extension of Picard 2-stacks,
and in the second Appendix we sketch the proof that the fibered sum of Picard
2-stacks satisfies the universal propert
Torsion and the Gravitational Interaction
By using a nonholonomous-frame formulation of the general covariance
principle, seen as an active version of the strong equivalence principle, an
analysis of the gravitational coupling prescription in the presence of
curvature and torsion is made. The coupling prescription implied by this
principle is found to be always equivalent with that of general relativity, a
result that reinforces the completeness of this theory, as well as the
teleparallel point of view according to which torsion does not represent
additional degrees of freedom for gravity, but simply an alternative way of
representing the gravitational field.Comment: Version 2: minor presentation changes, a reference added, 11 pages
(IOP style
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