Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 82-96). Available also in a digital version from Dissertation Abstracts.

Not available / text

The Kodama state is unique in being an exact solution to all the constraints of quantum gravity that also has a well defined semi-classical interpretation as the quantum version of a classical spacetime, namely de Sitter or anti-de sitter space. Despite this, the state fails to pass some of the key tests of a physically realistic quantum state. In an attempt to resolve this problem, we track down the root of the problem to a choice for a particular parameter: the Immirzi parameter. The Kodama state takes this parameter to be complex, whereas modern formulations of canonical quantum gravity require that the parameter is real. We generalize the Kodama state to real values of the Immirzi parameter, and find that the generalization opens up a large Hilbert space of states, one of which can be directly interpreted as particular slicing of de Sitter space. We then show that these states resolve, or are expected to resolve many of the problems associated with the original version of Kodama state. In order to resolve the interpretation of the multitude of states, we develop a new model of covariant classical and quantum gravity where the full Lorentz group is retained as a local symmetry group, and the canonical evolution generated by the constraints has a close relation to a larger group: that de Sitter group. This formalism gives strong evidence that the multitude of generalized Kodama states can be unified into a single quantum state that is quantum de Sitter space. / text

In this thesis I present a mathematical tool for understanding the spin networks that arise from the study of the loop states of quantum gravity. The spin networks that arise in quantum gravity possess more information than the original spin networks of Penrose: they are embedded within a manifold and thus possess topological information. There are limited tools available for the study of this information. To remedy this I introduce a slightly modi ed mathematical object - Braided Ribbon Networks - and demonstrate that they can be related to spin networks in a consistent manner which preserves the di eomorphism invariant character of the loop states of quantum gravity. Given a consistent de nition of Braided Ribbon Networks I then relate them back to previous trinion based versions of Braided Ribbon Networks. Next, I introduce a consistent evolution for these networks based upon the duality of these networks to simplicial complexes. From here I demonstrate that there exists an invariant of this evolution and smooth deformations of the networks, which captures some of the topological information of the networks. The principle result of this program is presented next: that the invariants of the Braided Ribbon Networks can be transferred over to the original spin network states of loop quantum gravity. From here we represent other advances in the study of braided ribbon networks, accompanied by comments of their context given the consistent framework developed earlier including: the meaning of isolatable substructures, the particular structure of the capped three braids in trivalent braided ribbon networks and their application towards emergent particle physics, and the implications of the existence of microlocal topological structures in spin networks. Lastly we describe the current state of research in braided ribbon networks, the implications of this study on quantum gravity as a whole and future directions of research in the area.

Thesis (Ph.D.)--Tufts University, 2000. / Adviser: Lawrence H. Ford. Submitted to the Dept. of Physics and Astronomy. Includes bibliographical references (leaves 99-105). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

In this thesis we consider foundational elements of quantum gravity as well as it possible observable astrophysical effects. In particular investigate a background independent formulation of Matrix Theory. We discuss a background independent formulation of a holographic theory of quantum gravity. The present thesis incorporates the necessary background material on geometry of canonical quantum theory, holography and spacetime thermodynamics, Matrix theory, as well as our specific proposal for a dynamical theory of geometric quantum mechanics, as applied to Matrix theory. At the heart of this thesis is a new analysis of the conceptual problem of time and the closely related and phenomenologically relevant problem of vacuum energy in quantum gravity. We also present a discussion of some observational implications of this new viewpoint on the problem of vacuum energy. as well as a novel solution to the low entropy and arrow of time puzzles of the initial state of the Universe. Our approach derives from the physics of the specific generalization of Matrix theory as the basis for a quantum theory of gravity considered here. The particular dynamical state space of this theory, the infinite dimensional analogue of the Fubini-Study metric over a complex non-linear Grassmannian, has recently been studied by Michor and Mumford. The geodesic distance between any two points on this space is zero. Here we show that this mathematical result translates to a description of a hot, zero entropy state and an arrow of time after the Big Bang. This is modeled as a far from equilibrium, large fluctuation driven, "freezing by heating" metastable ordered phase transition of a non-linear dissipative dynamical system. We also consider an evaporating black hole in the presence of an extra spatial dimension would undergo an explosive phase of evaporation. We show that such an event, involving a primordial black hole, can produce a detectable, distinguishable electromagnetic pulse, signaling the existence of an extra dimension of size L â ¼ 10â 18 â 10â 20 m. We derive a generic relationship between the Lorentz factor of a pulse-producing "fireball" and the TeV energy scale. For an ordinary toroidally compactified extra dimension, transient radio-pulse searches probe the electroweak energy scale (â ¼0.1 TeV), enabling comparison with the Large Hadron Collider. / Ph. D.

This thesis is devoted to developing a group-theoretical approach towards quantum gravity in (Anti)-de Sitter spacetime. We start with a comprehensive review of the representation theory of de Sitter (dS) isometry group, focusing on the construction of unitary irreducible representations and the computation of characters. The three chapters that follow present the results of novel research conducted as a graduate student. Chapter 4 is based on [1]. We provide a general algebraic construction of higher spin quasinormal modes of de Sitter horizon and identify the boundary operator insertions that source the quasinormal modes from a local QFT point of view. Quasinormal modes of a single higher spin field in dSD furnish two nonunitary lowest-weight representations of the dS isometry group SO(1,D). We also show that quasinormal mode spectrums of higher spin fields are precisely encoded in the Harish-Chandra characters of the corresponding SO(1,D) unitary irreducible representations. Chapter 5 is based on work with D. Anninos, F. Denef and A. Law [2]. With potential application to constraining UV-complete microscopic models of de Sitter quantum gravity, we compute de Sitter entropy as the logarithm of the sphere path integral, for any possible low energy effective field theory containing a massless graviton, in arbitrary dimensions. The path integral is performed exactly at the one-loop level. The one-loop correction to the dS entropy is found to take a universal “bulk−edge” form, with the bulk part being an integral transformation of a Harish-Chandra character encoding quasinormal modes spectrum in a static patch of dS and the edge part being the same integral transformation of an edge character encoding degrees of freedom frozen on the dS horizon. In 3D de Sitter spacetime, the one-loop exact entropy is promoted to an all-loop exact result for truncated higher spin gravity, the latter admitting an SL(n,C) Chern-Simons formulation with n being the spin cut-off. Chapter 6 is based on [3]. Inspired by [2], we revisit the one-loop partition function of any higher spin field in (d + 1)-dimensional Anti-de Sitter spacetime and show that it can be universally expressed as an integral transform of an SO(2, d) bulk character and an SO(2, d − 2) edge character. We apply this character integral formula to various higherspin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters, leading to striking agreement with the predictions of higher spin holography. We also comment on the relation between our character integral formula and Rindler-AdS [4] thermal partition functions.

Quantum mechanics is usually formulated in terms of a single Hilbert space and observables are defined as operators on this space. Attempts to describe entire spacetimes and their resident matter in this way often encounter paradoxes. For example, it has been argued that an observer falling into a black hole may be able to witness deviations from unitary, violations of semi-classical quantum field theory, and the like. This thesis argues that the essential problem is the insistence on the use of a single, global Hilbert space, because in general it may be that a physical observer cannot causally probe all of the information described by this space due to the presence of horizons. Instead, one could try to define unitary quantum physics directly in terms of the information causally accessible to particular observers. This thesis makes steps toward a systematization of this idea. Given an observer on a timelike worldline, I construct coordinates which (in good cases) cover precisely the set of events to which she can send and then receive a signal. These coordinates have spatial sections parametrized by her proper time, and the metric manifestly encodes the equivalence principle in the sense that it is flat along her worldline. To describe the quantum theory of fields according to these observers, I define Hilbert spaces in terms of field configurations on these spatial sections and show how to implement unitary time-evolution along proper time. I explain how to compare the observations of a pair of observers, and how to obtain the description according to some particular observer given some a priori global description. In this sense, the program outlined here constructs a manifestly unitary description of the events which the observer can causally probe. I give a number of explicit examples of the coordinates, and show how the quantum theory works for a uniformly accelerated observer in flat spacetime and for an inertial (co-moving) observer in an inflating universe. / text