56 research outputs found
Non-commutative holonomies in 2+1 LQG and Kauffman's brackets
We investigate the canonical quantization of 2+1 gravity with {\Lambda} > 0
in the canonical framework of LQG. A natural regularization of the constraints
of 2+1 gravity can be defined in terms of the holonomies of A\pm = A \PM
\surd{\Lambda}e, where the SU(2) connection A and the triad field e are the
conjugated variables of the theory. As a first step towards the quantization of
these constraints we study the canonical quantization of the holonomy of the
connection A_{\lambda} = A + {\lambda}e acting on spin network links of the
kinematical Hilbert space of LQG. We provide an explicit construction of the
quantum holonomy operator, exhibiting a close relationship between the action
of the quantum holonomy at a crossing and Kauffman's q-deformed crossing
identity. The crucial difference is that the result is completely described in
terms of standard SU(2) spin network states.Comment: 4 pages; Proceedings of Loops'11, Madrid, to appear in Journal of
Physics: Conference Series (JPCS
CFT/Gravity Correspondence on the Isolated Horizon
A quantum isolated horizon can be modelled by an SU(2) Chern-Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localised at the horizon which satisfy a Kac-Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational flux degrees of freedom in terms of the zero modes of the Kac-Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new nongeometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein's holographic bound for an imaginary Immirzi parameter. This allows us to recover the Bekenstein-Hawking entropy formula without the large quantum gravity corrections associated with the number of punctures. © 2014 The Authors
Higher spin dynamics in gravity and w1+∞ celestial symmetries
In this paper we extract from a large-r expansion of the vacuum Einstein's equations a dynamical system governing the time evolution of an infinity of higher-spin charges. Upon integration, we evaluate the canonical action of these charges on the gravity phase space. The truncation of this action to quadratic order and the associated charge conservation laws yield an infinite tower of soft theorems. We show that the canonical action of the higher spin charges on gravitons in a conformal primary basis, as well as conformally soft gravitons reproduces the higher spin celestial symmetries derived from the operator product expansion. Finally, we give direct evidence that these charges form a canonical representation of a w1+∞ loop algebra on the gravitational phase space
Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
A detailed analysis of the spherically symmetric isolated horizon system is
performed in terms of the connection formulation of general relativity. The
system is shown to admit a manifestly SU(2) invariant formulation where the
(effective) horizon degrees of freedom are described by an SU(2) Chern-Simons
theory. This leads to a more transparent description of the quantum theory in
the context of loop quantum gravity and modifications of the form of the
horizon entropy.Comment: 30 pages, 1 figur
Entropy in the Classical and Quantum Polymer Black Hole Models
We investigate the entropy counting for black hole horizons in loop quantum
gravity (LQG). We argue that the space of 3d closed polyhedra is the classical
counterpart of the space of SU(2) intertwiners at the quantum level. Then
computing the entropy for the boundary horizon amounts to calculating the
density of polyhedra or the number of intertwiners at fixed total area.
Following the previous work arXiv:1011.5628, we dub these the classical and
quantum polymer models for isolated horizons in LQG. We provide exact
micro-canonical calculations for both models and we show that the classical
counting of polyhedra accounts for most of the features of the intertwiner
counting (leading order entropy and log-correction), thus providing us with a
simpler model to further investigate correlations and dynamics. To illustrate
this, we also produce an exact formula for the dimension of the intertwiner
space as a density of "almost-closed polyhedra".Comment: 24 page
Canonical quantization of non-commutative holonomies in 2+1 loop quantum gravity
In this work we investigate the canonical quantization of 2+1 gravity with
cosmological constant in the canonical framework of loop quantum
gravity. The unconstrained phase space of gravity in 2+1 dimensions is
coordinatized by an SU(2) connection and the canonically conjugate triad
field . A natural regularization of the constraints of 2+1 gravity can be
defined in terms of the holonomies of . As a first step
towards the quantization of these constraints we study the canonical
quantization of the holonomy of the connection on the
kinematical Hilbert space of loop quantum gravity. The holonomy operator
associated to a given path acts non trivially on spin network links that are
transversal to the path (a crossing). We provide an explicit construction of
the quantum holonomy operator. In particular, we exhibit a close relationship
between the action of the quantum holonomy at a crossing and Kauffman's
q-deformed crossing identity. The crucial difference is that (being an operator
acting on the kinematical Hilbert space of LQG) the result is completely
described in terms of standard SU(2) spin network states (in contrast to
q-deformed spin networks in Kauffman's identity). We discuss the possible
implications of our result.Comment: 19 pages, references added. Published versio
Different formation kinetics and photoisomerization behavior of self-assembled monolayers of thiols and dithiolanes bearing azobenzene moieties
Self-assembled monolayers (SAMs) containing azobenzene moieties are very attractive for a wide range of applications, including molecular electronics and photonics, bio-interface engineering and sensoring. However, very little is known about the aggregation and photoswitching behavior that azobenzene units undergo during the SAM formation process. Here, we demonstrate that the formation of thiol based SAMs containing azobenzenes (denoted as AzoSH) on gold surfaces is characterised by a two step adsorption kinetics, while a three-step assembly process has been identified for dithiolane-based SAMs containing azobenzenes (denoted AzoSS). The H-aggregation on the AzoSS SAMs was found to be remarkably dependent on the time of self-assembly, with less aggregation as a function of time. While photoisomerization of the AzoSH was suppressed for all different assembly times, the reversible trans–cis photoisomerization of AzoSS SAMs formed over 24 hours was clearly observed upon alternating UV and Vis light irradiation. We contend that detailed information on formation kinetics and related optical properties is of crucial importance for elucidating the photoswitching capabilities of azobenzene based SAMs
A Note on the Symmetry Reduction of SU(2) on Horizons of Various Topologies
It is known that the SU(2) degrees of freedom manifest in the description of
the gravitational field in loop quantum gravity are generally reduced to U(1)
degrees of freedom on an isolated horizon. General relativity also allows
black holes with planar, toroidal, or higher genus topology for their horizons.
These solutions also meet the criteria for an isolated horizon, save for the
topological criterion, which is not crucial. We discuss the relevant
corresponding symmetry reduction for black holes of various topologies (genus 0
and ) here and discuss its ramifications to black hole entropy within
the loop quantum gravity paradigm. Quantities relevant to the horizon theory
are calculated explicitly using a generalized ansatz for the connection and
densitized triad, as well as utilizing a general metric admitting hyperbolic
sub-spaces. In all scenarios, the internal symmetry may be reduced to
combinations of U(1).Comment: 13 pages, two figures. Version 2 has several references updated and
added, as well as some minor changes to the text. Accepted for publication in
Class. Quant. Gra
Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
A dual formulation of group field theories, obtained by a Fourier transform
mapping functions on a group to functions on its Lie algebra, has been proposed
recently. In the case of the Ooguri model for SO(4) BF theory, the variables of
the dual field variables are thus so(4) bivectors, which have a direct
interpretation as the discrete B variables. Here we study a modification of the
model by means of a constraint operator implementing the simplicity of the
bivectors, in such a way that projected fields describe metric tetrahedra. This
involves a extension of the usual GFT framework, where boundary operators are
labelled by projected spin network states. By construction, the Feynman
amplitudes are simplicial path integrals for constrained BF theory. We show
that the spin foam formulation of these amplitudes corresponds to a variant of
the Barrett-Crane model for quantum gravity. We then re-examin the arguments
against the Barrett-Crane model(s), in light of our construction.Comment: revtex, 24 page
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