692 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
Polymer Parametrised Field Theory
Free scalar field theory on 2 dimensional flat spacetime, cast in
diffeomorphism invariant guise by treating the inertial coordinates of the
spacetime as dynamical variables, is quantized using LQG type `polymer'
representations for the matter field and the inertial variables. The quantum
constraints are solved via group averaging techniques and, analogous to the
case of spatial geometry in LQG, the smooth (flat) spacetime geometry is
replaced by a discrete quantum structure. An overcomplete set of Dirac
observables, consisting of (a) (exponentials of) the standard free scalar field
creation- annihilation modes and (b) canonical transformations corresponding to
conformal isometries, are represented as operators on the physical Hilbert
space. None of these constructions suffer from any of the `triangulation'
dependent choices which arise in treatments of LQG. In contrast to the standard
Fock quantization, the non- Fock nature of the representation ensures that the
algebra of conformal isometries as well as that of spacetime diffeomorphisms
are represented in an anomaly free manner. Semiclassical states can be analysed
at the gauge invariant level. It is shown that `physical weaves' necessarily
underly such states and that such states display semiclassicality with respect
to, at most, a countable subset of the (uncountably large) set of observables
of type (a). The model thus offers a fertile testing ground for proposed
definitions of quantum dynamics as well as semiclassical states in LQG.Comment: 44 pages, no figure
Polymer quantization of the free scalar field and its classical limit
Building on prior work, a generally covariant reformulation of free scalar
field theory on the flat Lorentzian cylinder is quantized using Loop Quantum
Gravity (LQG) type `polymer' representations. This quantization of the {\em
continuum} classical theory yields a quantum theory which lives on a discrete
spacetime lattice. We explicitly construct a state in the polymer Hilbert space
which reproduces the standard Fock vacuum- two point functions for long
wavelength modes of the scalar field. Our construction indicates that the
continuum classical theory emerges under coarse graining. All our
considerations are free of the "triangulation" ambiguities which plague
attempts to define quantum dynamics in LQG. Our work constitutes the first
complete LQG type quantization of a generally covariant field theory together
with a semi-classical analysis of the true degrees of freedom and thus provides
a perfect infinite dimensional toy model to study open issues in LQG,
particularly those pertaining to the definition of quantum dynamics.Comment: 58 page
I/O-Efficient Algorithms for Contour Line Extraction and Planar Graph Blocking
For a polyhedral terrain C, the contour at z-coordinate h, denoted Ch, is defined to be the intersection of the plane z = h with C. In this paper, we study the contour-line extraction problem, where we want to preprocess C into a data structure so that given a query z-coordinate h, we can report Ch quickly. This is a central problem that arises in geographic information systems (GIS), where terrains are often stored as Triangular Irregular Networks (TINS). We present an I/O-optimal algorithm for this problem which stores a terrain C with N vertices using O(N/B) blocks, where B is the size of a disk block, so that for any query h, the contour ch can be computed using o(log, N + I&l/B) I/O operations, where l&l denotes the size of Ch.
We also present en improved algorithm for a more general problem of blocking bounded-degree planar graphs such as TINS (i.e., storing them on disk so that any graph traversal algorithm can traverse the graph in an I/O-efficient manner), and apply it to two problms that arise in GIS
Synthetic experiments in the benzopyrone series. Part XXI. Isomerisation of C-(6 or 8)-methyl-5: 7-dihydroxy chromones
This article does not have an abstract
The graviton vacuum as a distributional state in kinematic Loop Quantum Gravity
The quantum behaviour of weak gravitational fields admits an adequate, albeit
approximate, description by those graviton states in which the expectation
values and fluctuations of the linearised gravitational field are small. Such
states must approximate corresponding states in full quantum gravity. We
analyse the nature of this approximation for the graviton vacuum state in the
context of kinematical Loop Quantum Gravity (LQG) wherein the constraints are
ignored. We identify the graviton vacuum state with kinematically
non-normalizable, distributional states in LQG by demanding that relations
between linearised operator actions on the former are mirrored by those of
their non-linear counterparts on the latter. We define a semi- norm on the
space of kinematical distributions and show that the identification is
approximate upto distributions which are small in this semi-norm. We argue that
our candidate states are annihilated by the linearised constraints (expressed
as operators in the full theory) to leading order in the parameter
characterising the approximation. This suggests the possibility, in a scheme
such as ours, of solving the full constraints order by order in this parameter.
The main drawback of our considerations is that they depend on certain
auxilliary constructions which, though mathematically well defined, do not
arise from physical insight. Our work is an attempt to implement an earlier
proposal of Iwasaki and Rovelli.Comment: 44 pages, no figure
Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse
We present an anomaly-free Dirac constraint quantization of the
string-inspired dilatonic gravity (the CGHS model) in an open 2-dimensional
spacetime. We show that the quantum theory has the same degrees of freedom as
the classical theory; namely, all the modes of the scalar field on an auxiliary
flat background, supplemented by a single additional variable corresponding to
the primordial component of the black hole mass. The functional Heisenberg
equations of motion for these dynamical variables and their canonical
conjugates are linear, and they have exactly the same form as the corresponding
classical equations. A canonical transformation brings us back to the physical
geometry and induces its quantization.Comment: 37 pages, LATEX, no figures, submitted to Physical Review
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