1,196 research outputs found
Kruskal coordinates as canonical variables for Schwarzschild black holes
We derive a transformation from the usual ADM metric-extrinsic curvature
variables on the phase space of Schwarzschild black holes, to new canonical
variables which have the interpretation of Kruskal coordinates. We explicitly
show that this transformation is non-singular, even at the horizon. The
constraints of the theory simplify in terms of the new canonical variables and
are equivalent to the vanishing of the canonical momenta. Our work is based on
earlier seminal work by Kuchar in which he reconstructed curvature coordinates
and a mass function from spherically symmetric canonical data. The key feature
in our construction of a nonsingular canonical transformation to Kruskal
variables, is the scaling of the curvature coordinate variables by the mass
function rather than by the mass at left spatial infinity.Comment: 18 pages, no figure
Classical and quantum geometrodynamics of 2d vacuum dilatonic black holes
We perform a canonical analysis of the system of 2d vacuum dilatonic black
holes. Our basic variables are closely tied to the spacetime geometry and we do
not make the field redefinitions which have been made by other authors. We
present a careful discssion of asymptotics in this canonical formalism.
Canonical transformations are made to variables which (on shell) have a clear
spacetime significance. We are able to deduce the location of the horizon on
the spatial slice (on shell) from the vanishing of a combination of canonical
data. The constraints dramatically simplify in terms of the new canonical
variables and quantization is easy. The physical interpretation of the variable
conjugate to the ADM mass is clarified. This work closely parallels that done
by Kucha{\v r} for the vacuum Schwarzschild black holes and is a starting point
for a similar analysis, now in progress, for the case of a massless scalar
field conformally coupled to a 2d dilatonic black hole.Comment: 21 pages, latex fil
ScALPEL: A Scalable Adaptive Lightweight Performance Evaluation Library for application performance monitoring
As supercomputers continue to grow in scale and capabilities, it is becoming
increasingly difficult to isolate processor and system level causes of
performance degradation. Over the last several years, a significant number of
performance analysis and monitoring tools have been built/proposed. However,
these tools suffer from several important shortcomings, particularly in
distributed environments. In this paper we present ScALPEL, a Scalable Adaptive
Lightweight Performance Evaluation Library for application performance
monitoring at the functional level. Our approach provides several distinct
advantages. First, ScALPEL is portable across a wide variety of architectures,
and its ability to selectively monitor functions presents low run-time
overhead, enabling its use for large-scale production applications. Second, it
is run-time configurable, enabling both dynamic selection of functions to
profile as well as events of interest on a per function basis. Third, our
approach is transparent in that it requires no source code modifications.
Finally, ScALPEL is implemented as a pluggable unit by reusing existing
performance monitoring frameworks such as Perfmon and PAPI and extending them
to support both sequential and MPI applications.Comment: 10 pages, 4 figures, 2 table
Functional evolution of quantum cylindrical waves
Kucha{\v{r}} showed that the quantum dynamics of (1 polarization) cylindrical
wave solutions to vacuum general relativity is determined by that of a free
axially-symmetric scalar field along arbitrary axially-symmetric foliations of
a fixed flat 2+1 dimensional spacetime. We investigate if such a dynamics can
be defined {\em unitarily} within the standard Fock space quantization of the
scalar field.
Evolution between two arbitrary slices of an arbitrary foliation of the flat
spacetime can be built out of a restricted class of evolutions (and their
inverses). The restricted evolution is from an initial flat slice to an
arbitrary (in general, curved) slice of the flat spacetime and can be
decomposed into (i) `time' evolution in which the spatial Minkowskian
coordinates serve as spatial coordinates on the initial and the final slice,
followed by (ii) the action of a spatial diffeomorphism of the final slice on
the data obtained from (i). We show that although the functional evolution of
(i) is unitarily implemented in the quantum theory, generic spatial
diffeomorphisms of (ii) are not. Our results imply that a Tomanaga-Schwinger
type functional evolution of quantum cylindrical waves is not a viable concept
even though, remarkably, the more limited notion of functional evolution in
Kucha{\v{r}}'s `half parametrized formalism' is well-defined.Comment: Replaced with published versio
Dirac Quantization of Parametrized Field Theory
Parametrized field theory (PFT) is free field theory on flat spacetime in a
diffeomorphism invariant disguise. It describes field evolution on arbitrary
foliations of the flat spacetime instead of only the usual flat ones, by
treating the `embedding variables' which describe the foliation as dynamical
variables to be varied in the action in addition to the scalar field. A formal
Dirac quantization turns the constraints of PFT into functional Schrodinger
equations which describe evolution of quantum states from an arbitrary Cauchy
slice to an infinitesimally nearby one.This formal Schrodinger picture- based
quantization is unitarily equivalent to the standard Heisenberg picture based
Fock quantization of the free scalar field if scalar field evolution along
arbitrary foliations is unitarily implemented on the Fock space. Torre and
Varadarajan (TV) showed that for generic foliations emanating from a flat
initial slice in spacetimes of dimension greater than 2, evolution is not
unitarily implemented, thus implying an obstruction to Dirac quantization.
We construct a Dirac quantization of PFT,unitarily equivalent to the standard
Fock quantization, using techniques from Loop Quantum Gravity (LQG) which are
powerful enough to super-cede the no- go implications of the TV results. The
key features of our quantization include an LQG type representation for the
embedding variables, embedding dependent Fock spaces for the scalar field, an
anomaly free representation of (a generalization of) the finite transformations
generated by the constraints and group averaging techniques. The difference
between 2 and higher dimensions is that in the latter, only finite gauge
transformations are defined in the quantum theory, not the infinitesimal ones.Comment: 33 page
A quantum logical and geometrical approach to the study of improper mixtures
We study improper mixtures from a quantum logical and geometrical point of
view. Taking into account the fact that improper mixtures do not admit an
ignorance interpretation and must be considered as states in their own right,
we do not follow the standard approach which considers improper mixtures as
measures over the algebra of projections. Instead of it, we use the convex set
of states in order to construct a new lattice whose atoms are all physical
states: pure states and improper mixtures. This is done in order to overcome
one of the problems which appear in the standard quantum logical formalism,
namely, that for a subsystem of a larger system in an entangled state, the
conjunction of all actual properties of the subsystem does not yield its actual
state. In fact, its state is an improper mixture and cannot be represented in
the von Neumann lattice as a minimal property which determines all other
properties as is the case for pure states or classical systems. The new lattice
also contains all propositions of the von Neumann lattice. We argue that this
extension expresses in an algebraic form the fact that -alike the classical
case- quantum interactions produce non trivial correlations between the
systems. Finally, we study the maps which can be defined between the extended
lattice of a compound system and the lattices of its subsystems.Comment: submitted to the Journal of Mathematical Physic
- …