146 research outputs found
Spin Networks for Non-Compact Groups
Spin networks are natural generalization of Wilson loops functionals. They
have been extensively studied in the case where the gauge group is compact and
it has been shown that they naturally form a basis of gauge invariant
observables. Physically the restriction to compact gauge group is enough for
the study of Yang-mills theories, however it is well known that non-compact
groups naturally arise as internal gauge groups for Lorentzian gravity models.
In this context a proper construction of gauge invariant observables is needed.
The purpose of this work is to define the notion of spin network states for
non-compact groups. We first built, by a careful gauge fixing procedure, a
natural measure and a Hilbert space structure on the space of gauge invariant
graph connection. Spin networks are then defined as generalized eigenvectors of
a complete set of hermitic commuting operators. We show how the delicate issue
of taking the quotient of a space by non compact groups can be address in term
of algebraic geometry. We finally construct the full Hilbert space containing
all spin network states. Having in mind application to gravity we illustrate
our results for the groups SL(2,R), SL(2,C).Comment: 43pages, many figures, some comments adde
Relating Covariant and Canonical Approaches to Triangulated Models of Quantum Gravity
In this paper explore the relation between covariant and canonical approaches
to quantum gravity and theory. We will focus on the dynamical
triangulation and spin-foam models, which have in common that they can be
defined in terms of sums over space-time triangulations. Our aim is to show how
we can recover these covariant models from a canonical framework by providing
two regularisations of the projector onto the kernel of the Hamiltonian
constraint. This link is important for the understanding of the dynamics of
quantum gravity. In particular, we will see how in the simplest dynamical
triangulations model we can recover the Hamiltonian constraint via our
definition of the projector. Our discussion of spin-foam models will show how
the elementary spin-network moves in loop quantum gravity, which were
originally assumed to describe the Hamiltonian constraint action, are in fact
related to the time-evolution generated by the constraint. We also show that
the Immirzi parameter is important for the understanding of a continuum limit
of the theory.Comment: 28 pages, 10 figure
On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables
We discuss various features and details of two versions of the Barrett-Crane
spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian
model and second of the SL(2,C)-symmetric Lorentzian version in which all
tetrahedra are space-like. Recently, Livine and Oriti proposed to introduce a
causal structure into the Lorentzian Barrett--Crane model from which one can
construct a path integral that corresponds to the causal (Feynman) propagator.
We show how to obtain convergent integrals for the 10j-symbols and how a
dimensionless constant can be introduced into the model. We propose a `Wick
rotation' which turns the rapidly oscillating complex amplitudes of the Feynman
path integral into positive real and bounded weights. This construction does
not yet have the status of a theorem, but it can be used as an alternative
definition of the propagator and makes the causal model accessible by standard
numerical simulation algorithms. In addition, we identify the local symmetries
of the models and show how their four-simplex amplitudes can be re-expressed in
terms of the ordinary relativistic 10j-symbols. Finally, motivated by possible
numerical simulations, we express the matrix elements that are defined by the
model, in terms of the continuous connection variables and determine the most
general observable in the connection picture. Everything is done on a fixed
two-complex.Comment: 22 pages, LaTeX 2e, 1 figur
A diagnostic real-time PCR assay for the rapid identification of the tomato-potato psyllid, Bactericera cockerelli (Sulc, 1909) and development of a psyllid barcoding database
The accurate and rapid identification of insect pests is an important step in the prevention and control of outbreaks in areas that are otherwise pest free. The potato-tomato psyllid Bactericera cockerelli (Sulc, 1909) is the main vector of 'Candidatus Liberibacter solanacearum' on potato and tomato crops in North America and New Zealand; and is considered a threat for introduction in Europe and other pest-free regions. This study describes the design and validation of the first species-specific TaqMan probe-based real-time PCR assay, targeting the ITS2 gene region of B. cockerelli. The assay detected B. cockerelli genomic DNA from adults, immatures, and eggs, with 100% accuracy. This assay also detected DNA from cloned plasmids containing the ITS2 region of B. cockerelli with 100% accuracy. The assay showed 0% false positives when tested on genomic and cloned DNA from 73 other psyllid species collected from across Europe, New Zealand, Mexico and the USA. This included 8 other species in the Bactericera genus and the main vectors of 'Candidatus Liberibacter solanacearum' worldwide. The limit of detection for this assay at optimum conditions was 0.000001ng DNA (similar to 200 copies) of ITS2 DNA which equates to around a 1:10000 dilution of DNA from one single adult specimen. This assay is the first real-time PCR based method for accurate, robust, sensitive and specific identification of B. cockerelli from all life stages. It can be used as a surveillance and monitoring tool to further study this important crop pest and to aid the prevention of outbreaks, or to prevent their spread after establishment in new areas
Positivity of Spin Foam Amplitudes
The amplitude for a spin foam in the Barrett-Crane model of Riemannian
quantum gravity is given as a product over its vertices, edges and faces, with
one factor of the Riemannian 10j symbols appearing for each vertex, and simpler
factors for the edges and faces. We prove that these amplitudes are always
nonnegative for closed spin foams. As a corollary, all open spin foams going
between a fixed pair of spin networks have real amplitudes of the same sign.
This means one can use the Metropolis algorithm to compute expectation values
of observables in the Riemannian Barrett-Crane model, as in statistical
mechanics, even though this theory is based on a real-time (e^{iS}) rather than
imaginary-time (e^{-S}) path integral. Our proof uses the fact that when the
Riemannian 10j symbols are nonzero, their sign is positive or negative
depending on whether the sum of the ten spins is an integer or half-integer.
For the product of 10j symbols appearing in the amplitude for a closed spin
foam, these signs cancel. We conclude with some numerical evidence suggesting
that the Lorentzian 10j symbols are always nonnegative, which would imply
similar results for the Lorentzian Barrett-Crane model.Comment: 15 pages LaTeX. v3: Final version, with updated conclusions and other
minor changes. To appear in Classical and Quantum Gravity. v4: corrects # of
samples in Lorentzian tabl
Three dimensional loop quantum gravity: physical scalar product and spin foam models
In this paper, we address the problem of the dynamics in three dimensional
loop quantum gravity with zero cosmological constant. We construct a rigorous
definition of Rovelli's generalized projection operator from the kinematical
Hilbert space--corresponding to the quantization of the infinite dimensional
kinematical configuration space of the theory--to the physical Hilbert space.
In particular, we provide the definition of the physical scalar product which
can be represented in terms of a sum over (finite) spin-foam amplitudes.
Therefore, we establish a clear-cut connection between the canonical
quantization of three dimensional gravity and spin-foam models. We emphasize
two main properties of the result: first that no cut-off in the kinematical
degrees of freedom of the theory is introduced (in contrast to standard
`lattice' methods), and second that no ill-defined sum over spins (`bubble'
divergences) are present in the spin foam representation.Comment: Typos corrected, version appearing in Class. Quant. Gra
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
A proposal for analyzing the classical limit of kinematic loop gravity
We analyze the classical limit of kinematic loop quantum gravity in which the
diffeomorphism and hamiltonian constraints are ignored. We show that there are
no quantum states in which the primary variables of the loop approach, namely
the SU(2) holonomies along {\em all} possible loops, approximate their
classical counterparts. At most a countable number of loops must be specified.
To preserve spatial covariance, we choose this set of loops to be based on
physical lattices specified by the quasi-classical states themselves. We
construct ``macroscopic'' operators based on such lattices and propose that
these operators be used to analyze the classical limit. Thus, our aim is to
approximate classical data using states in which appropriate macroscopic
operators have low quantum fluctuations.
Although, in principle, the holonomies of `large' loops on these lattices
could be used to analyze the classical limit, we argue that it may be simpler
to base the analysis on an alternate set of ``flux'' based operators. We
explicitly construct candidate quasi-classical states in 2 spatial dimensions
and indicate how these constructions may generalize to 3d. We discuss the less
robust aspects of our proposal with a view towards possible modifications.
Finally, we show that our proposal also applies to the diffeomorphism invariant
Rovelli model which couples a matter reference system to the Hussain Kucha{\v
r} model.Comment: Replaced with substantially revised versio
Spin Foam Models of Riemannian Quantum Gravity
Using numerical calculations, we compare three versions of the Barrett-Crane
model of 4-dimensional Riemannian quantum gravity. In the version with face and
edge amplitudes as described by De Pietri, Freidel, Krasnov, and Rovelli, we
show the partition function diverges very rapidly for many triangulated
4-manifolds. In the version with modified face and edge amplitudes due to Perez
and Rovelli, we show the partition function converges so rapidly that the sum
is dominated by spin foams where all the spins labelling faces are zero except
for small, widely separated islands of higher spin. We also describe a new
version which appears to have a convergent partition function without drastic
spin-zero dominance. Finally, after a general discussion of how to extract
physics from spin foam models, we discuss the implications of convergence or
divergence of the partition function for other aspects of a spin foam model.Comment: 23 pages LaTeX; this version to appear in Classical and Quantum
Gravit
First report of ' Candidatus Liberibacter solanacearum' in the United Kingdom in the psyllid Trioza anthrisci
ORCID ID 0000-0003-2931-6116©2017 The Authors. This is an open access article, available to all readers online. New Disease Reports is a peer-reviewed, international, open-access electronic journal, published by the British Society for Plant Pathology
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