506 research outputs found
Consistent discretizations: the Gowdy spacetimes
We apply the consistent discretization scheme to general relativity
particularized to the Gowdy space-times. This is the first time the framework
has been applied in detail in a non-linear generally-covariant gravitational
situation with local degrees of freedom. We show that the scheme can be
correctly used to numerically evolve the space-times. We show that the
resulting numerical schemes are convergent and preserve approximately the
constraints as expected.Comment: 10 pages, 8 figure
Consistent discretization and loop quantum geometry
We apply the ``consistent discretization'' approach to general relativity
leaving the spatial slices continuous. The resulting theory is free of the
diffeomorphism and Hamiltonian constraints, but one can impose the
diffeomorphism constraint to reduce its space of solutions and the constraint
is preserved exactly under the discrete evolution. One ends up with a theory
that has as physical space what is usually considered the kinematical space of
loop quantum geometry, given by diffeomorphism invariant spin networks endowed
with appropriate rigorously defined diffeomorphism invariant measures and inner
products. The dynamics can be implemented as a unitary transformation and the
problem of time explicitly solved or at least reduced to as a numerical
problem. We exhibit the technique explicitly in 2+1 dimensional gravity.Comment: 4 pages, Revtex, no figure
17 ways to say yes:Toward nuanced tone of voice in AAC and speech technology
People with complex communication needs who use speech-generating devices have very little expressive control over their tone of voice. Despite its importance in human interaction, the issue of tone of voice remains all but absent from AAC research and development however. In this paper, we describe three interdisciplinary projects, past, present and future: The critical design collection Six Speaking Chairs has provoked deeper discussion and inspired a social model of tone of voice; the speculative concept Speech Hedge illustrates challenges and opportunities in designing more expressive user interfaces; the pilot project Tonetable could enable participatory research and seed a research network around tone of voice. We speculate that more radical interactions might expand frontiers of AAC and disrupt speech technology as a whole
Fundamental decoherence from relational time in discrete quantum gravity: Galilean covariance
We have recently argued that if one introduces a relational time in quantum
mechanics and quantum gravity, the resulting quantum theory is such that pure
states evolve into mixed states. The rate at which states decohere depends on
the energy of the states. There is therefore the question of how this can be
reconciled with Galilean invariance. More generally, since the relational
description is based on objects that are not Dirac observables, the issue of
covariance is of importance in the formalism as a whole. In this note we work
out an explicit example of a totally constrained, generally covariant system of
non-relativistic particles that shows that the formula for the relational
conditional probability is a Galilean scalar and therefore the decoherence rate
is invariant.Comment: 10 pages, RevTe
Dirac-like approach for consistent discretizations of classical constrained theories
We analyze the canonical treatment of classical constrained mechanical
systems formulated with a discrete time. We prove that under very general
conditions, it is possible to introduce nonsingular canonical transformations
that preserve the constraint surface and the Poisson or Dirac bracket
structure. The conditions for the preservation of the constraints are more
stringent than in the continuous case and as a consequence some of the
continuum constraints become second class upon discretization and need to be
solved by fixing their associated Lagrange multipliers. The gauge invariance of
the discrete theory is encoded in a set of arbitrary functions that appear in
the generating function of the evolution equations. The resulting scheme is
general enough to accommodate the treatment of field theories on the lattice.
This paper attempts to clarify and put on sounder footing a discretization
technique that has already been used to treat a variety of systems, including
Yang--Mills theories, BF-theory and general relativity on the lattice.Comment: 11 pages, RevTe
Uniform discretizations: a new approach for the quantization of totally constrained systems
We discuss in detail the uniform discretization approach to the quantization
of totally constrained theories. This approach allows to construct the
continuum theory of interest as a well defined, controlled, limit of well
behaved discrete theories. We work out several finite dimensional examples that
exhibit behaviors expected to be of importance in the quantization of gravity.
We also work out the case of BF theory. At the time of quantization, one can
take two points of view. The technique can be used to define, upon taking the
continuum limit, the space of physical states of the continuum constrained
theory of interest. In particular we show in models that it agrees with the
group averaging procedure when the latter exists. The technique can also be
used to compute, at the discrete level, conditional probabilities and the
introduction of a relational time. Upon taking the continuum limit one can show
that one reproduces results obtained by the use of evolving constants, and
therefore recover all physical predictions of the continuum theory. This second
point of view can also be used as a paradigm to deal with cases where the
continuum limit does not exist. There one would have discrete theories that at
least at certain scales reproduce the semiclassical properties of the theory of
interest. In this way the approach can be viewed as a generalization of the
Dirac quantization procedure that can handle situations where the latter fails.Comment: 17 pages, Revtex, no figures, published versio
Canonical quantization of general relativity in discrete space-times
It has long been recognized that lattice gauge theory formulations, when
applied to general relativity, conflict with the invariance of the theory under
diffeomorphisms. Additionally, the traditional lattice field theory approach
consists in fixing the gauge in a Euclidean action, which does not appear
appropriate for general relativity. We analyze discrete lattice general
relativity and develop a canonical formalism that allows to treat constrained
theories in Lorentzian signature space-times. The presence of the lattice
introduces a ``dynamical gauge'' fixing that makes the quantization of the
theories conceptually clear, albeit computationally involved. Among other
issues the problem of a consistent algebra of constraints is automatically
solved in our approach. The approach works successfully in other field theories
as well, including topological theories like BF theory. We discuss a simple
cosmological application that exhibits the quantum elimination of the
singularity at the big bang.Comment: 4 pages, RevTeX, no figures, final version to appear in Physical
Review Letter
Perturbative evolution of conformally flat initial data for a single boosted black hole
The conformally flat families of initial data typically used in numerical
relativity to represent boosted black holes are not those of a boosted slice of
the Schwarzschild spacetime. If such data are used for each black hole in a
collision, the emitted radiation will be partially due to the ``relaxation'' of
the individual holes to ``boosted Schwarzschild'' form. We attempt to compute
this radiation by treating the geometry for a single boosted conformally flat
hole as a perturbation of a Schwarzschild black hole, which requires the use of
second order perturbation theory. In this we attempt to mimic a previous
calculation we did for the conformally flat initial data for spinning holes. We
find that the boosted black hole case presents additional subtleties, and
although one can evolve perturbatively and compute radiated energies, it is
much less clear than in the spinning case how useful for the study of
collisions are the radiation estimates for the ``spurious energy'' in each
hole. In addition to this we draw some lessons on which frame of reference
appears as more favorable for computing black hole collisions in the close
limit approximation.Comment: 11 pages, RevTex, 4 figures included with psfig, to appear in PR
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