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

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 $(2|1)$-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 $p_{win}=\cos^2{\pi/8}\simeq0.8536$ of standard quantum mechanics. Case (3) crosses Tsirelson's bound with $p_{win}\simeq0.9265$. 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 adde

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} $U(1)\times U(1)\times U(1)$ 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 $U(1)\times U(1)\times U(1)$ 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} $U(1)\times U(1)\times U(1)$ 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

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