1,513 research outputs found
A Comment on the Degrees of Freedom in the Ashtekar Formulation for 2+1 Gravity
We show that the recent claim that the 2+1 dimensional Ashtekar formulation
for General Relativity has a finite number of physical degrees of freedom is
not correct.Comment: 6 pages LaTex, to appear in Classical and Quantum Gravit
On the resolution of the big bang singularity in isotropic Loop Quantum Cosmology
In contrast to previous work in the field, we construct the Loop Quantum
Cosmology (LQC) of the flat isotropic model with a massless scalar field in the
absence of higher order curvature corrections to the gravitational part of the
Hamiltonian constraint. The matter part of the constraint contains the inverse
triad operator which can be quantized with or without the use of a Thiemann-
like procedure. With the latter choice, we show that the LQC quantization is
identical to that of the standard Wheeler DeWitt theory (WDW) wherein there is
no singularity resolution. We argue that the former choice leads to singularity
resolution in the sense of a well defined, regular (backward) evolution through
and beyond the epoch where the size of the universe vanishes.
Our work along with that of the seminal work of Ashtekar, Pawlowski and Singh
(APS) clarifies the role, in singularity resolution, of the three `exotic'
structures in this LQC model, namely: curvature corrections, inverse triad
definitions and the `polymer' nature of the kinematic representation. We also
critically examine certain technical assumptions made by APS in their analysis
of WDW semiclassical states and point out some problems stemming from the
infrared behaviour of their wave functionsComment: 26 pages, no figure
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
Gravitons from a loop representation of linearised gravity
Loop quantum gravity is based on a classical formulation of 3+1 gravity in
terms of a real SU(2) connection. Linearization of this classical formulation
about a flat background yields a description of linearised gravity in terms of
a {\em real} connection. A `loop' representation,
in which holonomies of this connection are unitary operators, can be
constructed. These holonomies are not well defined operators in the standard
graviton Fock representation. We generalise our recent work on photons and U(1)
holonomies to show that Fock space gravitons are associated with distributional
states in the loop representation. Our results may
illuminate certain aspects of the much deeper (and as yet unkown,) relation
between gravitons and states in nonperturbative loop quantum gravity.
This work leans heavily on earlier seminal work by Ashtekar, Rovelli and
Smolin (ARS) on the loop representation of linearised gravity using {\em
complex} connections. In the last part of this work, we show that the loop
representation based on the {\em real} connection
also provides a useful kinematic arena in which it is possible to express the
ARS complex connection- based results in the mathematically precise language
currently used in the field.Comment: 23 pages, no figure
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
Tsirelson's bound and supersymmetric entangled states
A superqubit, belonging to a -dimensional super-Hilbert space,
constitutes the minimal supersymmetric extension of the conventional qubit. In
order to see whether superqubits are more nonlocal than ordinary qubits, we
construct a class of two-superqubit entangled states as a nonlocal resource in
the CHSH game. Since super Hilbert space amplitudes are Grassmann numbers, the
result depends on how we extract real probabilities and we examine three
choices of map: (1) DeWitt (2) Trigonometric (3) Modified Rogers. In cases (1)
and (2) the winning probability reaches the Tsirelson bound
of standard quantum mechanics. Case (3)
crosses Tsirelson's bound with . Although all states used
in the game involve probabilities lying between 0 and 1, case (3) permits other
changes of basis inducing negative transition probabilities.Comment: Updated to match published version. Minor modifications. References
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Van der Waerden calculus with commuting spinor variables and the Hilbert-Krein structure of the superspace
Working with anticommuting Weyl(or Mayorana) spinors in the framework of the
van der Waerden calculus is standard in supersymmetry. The natural frame for
rigorous supersymmetric quantum field theory makes use of operator-valued
superdistributions defined on supersymmetric test functions. In turn this makes
necessary a van der Waerden calculus in which the Grassmann variables
anticommute but the fermionic components are commutative instead of being
anticommutative. We work out such a calculus in view of applications to the
rigorous conceptual problems of the N=1 supersymmetric quantum field theory.Comment: 14 page
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