109 research outputs found
LQG for the Bewildered
We present a pedagogical introduction to the notions underlying the
connection formulation of General Relativity - Loop Quantum Gravity (LQG) -
with an emphasis on the physical aspects of the framework. We begin by
reviewing General Relativity and Quantum Field Theory, to emphasise the
similarities between them which establish a foundation upon which to build a
theory of quantum gravity. We then explain, in a concise and clear manner, the
steps leading from the Einstein-Hilbert action for gravity to the construction
of the quantum states of geometry, known as \emph{spin-networks}, which provide
the basis for the kinematical Hilbert space of quantum general relativity.
Along the way we introduce the various associated concepts of \emph{tetrads},
\emph{spin-connection} and \emph{holonomies} which are a pre-requisite for
understanding the LQG formalism. Having provided a minimal introduction to the
LQG framework, we discuss its applications to the problems of black hole
entropy and of quantum cosmology. A list of the most common criticisms of LQG
is presented, which are then tackled one by one in order to convince the reader
of the physical viability of the theory.
An extensive set of appendices provide accessible introductions to several
key notions such as the \emph{Peter-Weyl theorem}, \emph{duality} of
differential forms and \emph{Regge calculus}, among others. The presentation is
aimed at graduate students and researchers who have some familiarity with the
tools of quantum mechanics and field theory and/or General Relativity, but are
intimidated by the seeming technical prowess required to browse through the
existing LQG literature. Our hope is to make the formalism appear a little less
bewildering to the un-initiated and to help lower the barrier for entry into
the field.Comment: 87 pages, 15 figures, manuscript submitted for publicatio
Effective Theory of Braid Excitations of Quantum Geometry in terms of Feynman Diagrams
We study interactions amongst topologically conserved excitations of quantum
theories of gravity, in particular the braid excitations of four-valent spin
networks. These have been shown previously to propagate and interact under
evolution rules of spin foam models. We show that the dynamics of these braid
excitations can be described by an effective theory based on Feynman diagrams.
In this language, braids which are actively interacting are analogous to
bosons, in that the topological conservation laws permit them to be singly
created and destroyed. Exchanges of these excitations give rise to interactions
between braids which are charged under the topological conservation rules.Comment: 23 pages, 7 figures. Accepted by Nucl. Phys.
Propagation and interaction of chiral states in quantum gravity
We study the stability, propagation and interactions of braid states in
models of quantum gravity in which the states are four-valent spin networks
embedded in a topological three manifold and the evolution moves are given by
the dual Pachner moves. There are results for both the framed and unframed
case. We study simple braids made up of two nodes which share three edges,
which are possibly braided and twisted. We find three classes of such braids,
those which both interact and propagate, those that only propagate, and the
majority that do neither.Comment: 34 pages, 30 figures, typos corrected, 2 references added, to match
the version accepted for publication in Nucl. Phys.
Highly-improved lattice field-strength tensor
We derive an O(a^4)-improved lattice version of the continuum field-strength
tensor. Discretization errors are reduced via the combination of several clover
terms of various sizes, complemented by tadpole improvement. The resulting
improved field-strength tensor is used to construct O(a^4)-improved topological
charge and action operators. We compare the values attained by these operators
as we cool several configurations to self-duality with a previously defined
highly-improved action and assess the relative scale of the remaining
discretization errors.Comment: 22 pages, 7 postscript figure
Locality and Translations in Braided Ribbon Networks
An overview of microlocality in braided ribbon networks is presented.
Following this, a series of definitions are presented to explore the concept of
microlocality and the topology of ribbon networks. Isolated substructure of
ribbon networks are introduced, and a theorem is proven that allows them to be
relocated. This is followed by a demonstration of microlocal translations.
Additionally, an investigation into macrolocality and the implications of
invariants in braided ribbon networks are presented.Comment: 12 pages, 12 figure
Infinite Degeneracy of States in Quantum Gravity
The setting of Braided Ribbon Networks is used to present a general result in
spin-networks embedded in manifolds: the existence of an infinite number of
species of conserved quantities. Restricted to three-valent networks the number
of such conserved quantities in a given network is shown to be invariant
barring a single case. The implication of these conserved quantities is
discussed in the context of Loop Quantum Gravity.Comment: 10 pages, 14 figures, v2: some clarifications, no substantial change
FLIC-Overlap Fermions and Topology
APE smearing the links in the irrelevant operators of clover fermions
(Fat-Link Irrelevant Clover (FLIC) fermions) provides significant improvement
in the condition number of the Hermitian-Dirac operator and gives rise to a
factor of two savings in computing the overlap operator. This report
investigates the effects of using a highly-improved definition of the lattice
field-strength tensor F_mu_nu in the fermion action, made possible through the
use of APE-smeared fat links in the construction of the irrelevant operators.
Spurious double-zero crossings in the spectral flow of the Hermitian-Wilson
Dirac operator associated with lattice artifacts at the scale of the lattice
spacing are removed with FLIC fermions composed with an O(a^4)-improved lattice
field strength tensor. Hence, FLIC-Overlap fermions provide an additional
benefit to the overlap formalism: a correct realization of topology in the
fermion sector on the lattice.Comment: Lattice2002(chiral
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