Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

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In this dissertation we study the dynamics of loop quantum gravity and its applications. We propose a tunneling phenomenon of a black hole-white hole transition and derive an amplitude for such transition using the spinfoam framework. We investigate a special class of kinematical states for loop quantum gravity - Bell spin networks - and show that their entanglement entropy obeys the area law. We develop a new spinfoam vertex amplitude that has the correct semi-classical limit. We then apply this new amplitude to calculate the graviton propagator and a cosmological transition amplitude. The results of these calculations show feasibility of computations with the new amplitude and its viability as a spinfoam model. Finally, we use physical principles to radically constrain ambiguities in the cosmological dynamics and derive unique Hamiltonian dynamics for Friedmann-Robertson-Walker and Bianchi I cosmologies. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

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The aim of this thesis is to summarize some results in two approaches to studying how quantum gravity may be relevant for experiments. The first approach starts off by stating that one of the questions a theory of quantum gravity might address is how a large-scale universe can be constructed from discrete Planck-size elements. Starting from a discussion of the role of causal and foliation structure in causal dynamical triangulations, this approach leads to a formulation of a model based on graphs whose purpose is to uncover what kind organizational principle or structure might be responsible for endowing spacetime with manifold-like properties. Thus in this approach, experimental input used to constrain models for quantum gravity are observations of glaring large-scale properties of the universe such as the dimensionality or total size. The second approach considers the possible effects of quantum gravity on the propagation of particles. In particular, the focus is on understanding the physics of deformed special relativity when this novel symmetry is seen as a residual effect due to a gauge fixing from a higher dimensional system. Thus here the hope is to connect a proposal for quantum gravity phenomenology with precision experiments of particle properties. A synthesis of such complementary approaches would represent a consistent model for quantum gravity phenomenology and is the background goal for the work in this thesis. The extent to which such a synthesis can be described today is presented.

The aim of this thesis is to summarize some results in two approaches to studying how quantum gravity may be relevant for experiments. The first approach starts off by stating that one of the questions a theory of quantum gravity might address is how a large-scale universe can be constructed from discrete Planck-size elements. Starting from a discussion of the role of causal and foliation structure in causal dynamical triangulations, this approach leads to a formulation of a model based on graphs whose purpose is to uncover what kind organizational principle or structure might be responsible for endowing spacetime with manifold-like properties. Thus in this approach, experimental input used to constrain models for quantum gravity are observations of glaring large-scale properties of the universe such as the dimensionality or total size. The second approach considers the possible effects of quantum gravity on the propagation of particles. In particular, the focus is on understanding the physics of deformed special relativity when this novel symmetry is seen as a residual effect due to a gauge fixing from a higher dimensional system. Thus here the hope is to connect a proposal for quantum gravity phenomenology with precision experiments of particle properties. A synthesis of such complementary approaches would represent a consistent model for quantum gravity phenomenology and is the background goal for the work in this thesis. The extent to which such a synthesis can be described today is presented.

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.