1,624 research outputs found
Covariance and Time Regained in Canonical General Relativity
Canonical vacuum gravity is expressed in generally-covariant form in order
that spacetime diffeomorphisms be represented within its equal-time phase
space. In accordance with the principle of general covariance, the time mapping
{\T}: {\yman} \to {\rman} and the space mapping {\X}: {\yman} \to {\xman}
that define the Dirac-ADM foliation are incorporated into the framework of the
Hilbert variational principle. The resulting canonical action encompasses all
individual Dirac-ADM actions, corresponding to different choices of foliating
vacuum spacetimes by spacelike hypersurfaces. In this framework, spacetime
observables, namely, dynamical variables that are invariant under spacetime
diffeomorphisms, are not necessarily invariant under the deformations of the
mappings \T and \X, nor are they constants of the motion. Dirac observables
form only a subset of spacetime observables that are invariant under the
transformations of \T and \X and do not evolve in time. The conventional
interpretation of the canonical theory, due to Bergmann and Dirac, can be
recovered only by postulating that the transformations of the reference system
({\T},{\X}) have no measurable consequences. If this postulate is not deemed
necessary, covariant canonical gravity admits no classical problem of time.Comment: 41 pages, no figure
Proof of the Thin Sandwich Conjecture
We prove that the Thin Sandwich Conjecture in general relativity is valid,
provided that the data satisfy certain geometric
conditions. These conditions define an open set in the class of possible data,
but are not generically satisfied. The implications for the ``superspace''
picture of the Einstein evolution equations are discussed.Comment: 8 page
Embedding variables in finite dimensional models
Global problems associated with the transformation from the Arnowitt, Deser
and Misner (ADM) to the Kucha\v{r} variables are studied. Two models are
considered: The Friedmann cosmology with scalar matter and the torus sector of
the 2+1 gravity. For the Friedmann model, the transformations to the Kucha\v{r}
description corresponding to three different popular time coordinates are shown
to exist on the whole ADM phase space, which becomes a proper subset of the
Kucha\v{r} phase spaces. The 2+1 gravity model is shown to admit a description
by embedding variables everywhere, even at the points with additional symmetry.
The transformation from the Kucha\v{r} to the ADM description is, however,
many-to-one there, and so the two descriptions are inequivalent for this model,
too. The most interesting result is that the new constraint surface is free
from the conical singularity and the new dynamical equations are linearization
stable. However, some residual pathology persists in the Kucha\v{r}
description.Comment: Latex 2e, 29 pages, no figure
Covariant gauge fixing and Kuchar decomposition
The symplectic geometry of a broad class of generally covariant models is
studied. The class is restricted so that the gauge group of the models
coincides with the Bergmann-Komar group and the analysis can focus on the
general covariance. A geometrical definition of gauge fixing at the constraint
manifold is given; it is equivalent to a definition of a background (spacetime)
manifold for each topological sector of a model. Every gauge fixing defines a
decomposition of the constraint manifold into the physical phase space and the
space of embeddings of the Cauchy manifold into the background manifold (Kuchar
decomposition). Extensions of every gauge fixing and the associated Kuchar
decomposition to a neighbourhood of the constraint manifold are shown to exist.Comment: Revtex, 35 pages, no figure
Expression and Localization of CLC Chloride Transport Proteins in the Avian Retina
Members of the ubiquitously expressed CLC protein family of chloride channels and transporters play important roles in regulating cellular chloride and pH. The CLCs that function as Cl−/H+ antiporters, ClCs 3–7, are essential in particular for the acidification of endosomal compartments and protein degradation. These proteins are broadly expressed in the nervous system, and mutations that disrupt their expression are responsible for several human genetic diseases. Furthermore, knock-out of ClC3 and ClC7 in the mouse result in the degeneration of the hippocampus and the retina. Despite this evidence of their importance in retinal function, the expression patterns of different CLC transporters in different retinal cell types are as yet undescribed. Previous work in our lab has shown that in chicken amacrine cells, internal Cl− can be dynamic. To determine whether CLCs have the potential to participate, we used PCR and immunohistochemical techniques to examine CLC transporter expression in the chicken retina. We observed a high level of variation in the retinal expression levels and patterns among the different CLC proteins examined. These findings, which represent the first systematic investigation of CLC transporter expression in the retina, support diverse functions for the different CLCs in this tissue
Spin-orbit Scattering and the Kondo Effect
The effects of spin-orbit scattering of conduction electrons in the Kondo
regime are investigated theoretically. It is shown that due to time-reversal
symmetry, spin-orbit scattering does not suppress the Kondo effect, even though
it breaks spin-rotational symmetry, in full agreement with experiment. An
orbital magnetic field, which breaks time-reversal symmetry, leads to an
effective Zeeman splitting, which can be probed in transport measurements. It
is shown that, similar to weak-localization, this effect has anomalous magnetic
field and temperature dependence.Comment: 10 pages, RevTex, one postscript figure available on request from
[email protected]
Dirac's Observables for the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge
We define the {\it rest-frame instant form} of tetrad gravity restricted to
Christodoulou-Klainermann spacetimes. After a study of the Hamiltonian group of
gauge transformations generated by the 14 first class constraints of the
theory, we define and solve the multitemporal equations associated with the
rotation and space diffeomorphism constraints, finding how the cotriads and
their momenta depend on the corresponding gauge variables. This allows to find
quasi-Shanmugadhasan canonical transformation to the class of 3-orthogonal
gauges and to find the Dirac observables for superspace in these gauges.
The construction of the explicit form of the transformation and of the
solution of the rotation and supermomentum constraints is reduced to solve a
system of elliptic linear and quasi-linear partial differential equations. We
then show that the superhamiltonian constraint becomes the Lichnerowicz
equation for the conformal factor of the 3-metric and that the last gauge
variable is the momentum conjugated to the conformal factor. The gauge
transformations generated by the superhamiltonian constraint perform the
transitions among the allowed foliations of spacetime, so that the theory is
independent from its 3+1 splittings. In the special 3-orthogonal gauge defined
by the vanishing of the conformal factor momentum we determine the final Dirac
observables for the gravitational field even if we are not able to solve the
Lichnerowicz equation. The final Hamiltonian is the weak ADM energy restricted
to this completely fixed gauge.Comment: RevTeX file, 141 page
The Hamiltonian formulation of General Relativity: myths and reality
A conventional wisdom often perpetuated in the literature states that: (i) a
3+1 decomposition of space-time into space and time is synonymous with the
canonical treatment and this decomposition is essential for any Hamiltonian
formulation of General Relativity (GR); (ii) the canonical treatment
unavoidably breaks the symmetry between space and time in GR and the resulting
algebra of constraints is not the algebra of four-dimensional diffeomorphism;
(iii) according to some authors this algebra allows one to derive only spatial
diffeomorphism or, according to others, a specific field-dependent and
non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac
[Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in
"Gravitation: An Introduction to Current Research" (1962) 227] of the canonical
structure of GR are equivalent. We provide some general reasons why these
statements should be questioned. Points (i-iii) have been shown to be incorrect
in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly
re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that
points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation
of GR. We also demonstrate that ADM and Dirac formulations are related by a
transformation of phase-space variables from the metric to lapse
and shift functions and the three-metric , which is not canonical. This
proves that point (iv) is incorrect. Points (i-iii) are mere consequences of
using a non-canonical change of variables and are not an intrinsic property of
either the Hamilton-Dirac approach to constrained systems or Einstein's theory
itself.Comment: References are added and updated, Introduction is extended,
Subsection 3.5 is added, 83 pages; corresponds to the published versio
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