Thesis (Ph. D.)--University of Chicago, Department of Physics, August, 2003. / Includes bibliographical references. Also available on the Internet.

We construct a 4d Lorentzian spin foam model capable of describing both spacelike and timelike surfaces. To do so we use a coherent state approach inspired by the Riemannian FK model. Using the coherent state method we reproduce the results of the EPRL model for Euclidean tetrahedra and extend the model to include Lorentzian tetrahedra. The coherent states of spacelike/timelike triangles are found to correspond to elements of the discrete/continuous series of SU(1,1). It is found that the area spectrum of both spacelike and timelike surfaces is quantized. A path integral for the quantum theory is defined as a product of vertex amplitudes. The states corresponding to timelike triangles are constructed in a basis diagonalised with respect to a noncompact generator. A derivation of the matrix elements of the generators of SL(2,C) in this basis is provided.

We propose a Generalized Uncertainty Principle (GUP) consistent with String Theory, Black Hole Physics and Doubly Special Relativity. This modifies all quantum mechanical Hamiltonians and predicts quantum gravity corrections. We compute corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current. When applied to an elementary particle, it suggests that the space must be quantized, and that all measurable lengths are quantized in units of a fundamental length. We investigated whether GUP can explain the violation of the equivalence principle at small length scales that was observed experimentally. We investigated the consequences of GUP on Liouville theorem. We examined GUP effect on post inflation preheating, and show that it predicts an increase or a decrease in parametric resonance and a change in particle production. The effect of GUP on the creation of black holes is investigated to justify the experimental results from the Large Hadron Collider. / viii, 154 leaves ; 30 cm

The continuous, kinematical Hilbert space of loop quantum gravity is built upon a family of spaces $\mathcal{H}_\Gamma$, each associated to a different \textit{graph} $\Gamma$, i.e. a network of interconnected one-dimensional links $\l$, embedded within a spatial geometry. The kinematics of loop quantum gravity are well-established, but difficult problems remain for the dynamics. There are two steps in getting to the quantum theory from the classical one: first, the embedded graphs are used to define a smearing of the continuous gravitational fields to obtain a holonomy $h_\l$ and flux $\X_\l$ for each link of the graph, giving a phase space $P_\Gamma$; second, this phase space is quantized to yield a finite dimensional Hilbert space $\mathcal{H}_\Gamma$. The intermediate classical theory in terms of $P_\Gamma$ phase spaces remains largely unexplored, and here we endeavour to develop it. If we can find such a theory that is consistent with general relativity, then we will have a theory of gravity based upon finite-dimensional phase spaces that is nicely set up for quantization \`a la loop quantum gravity. To begin, we first review the basic elements of the quantum theory before introducing the classical phase space structure. Within this framework we show that there is a one-to-one correspondence between the data on a graph and an equivalence class of continuous geometries. We find that a particular member of each class, the spinning geometry, makes a promising candidate as a gauge choice to represent the $(h_\l, \X_\l)$ data in the continuous theory, helping us to formulate a dynamics for the discrete theory. Considering all of the possible graphs, it is important to know how we can evolve from one phase space into another, and how the dynamics in $P_\Gamma$ relates to the continuous evolution. There is a geometrical description of phase spaces where dynamics appears as a class of subspaces within a symplectic manifold. We use this picture to formulate a dynamics between $P_\Gamma$ phase spaces, and demonstrate this process on a simple model that mimics the case of full gravity. Following this, we study a system of point particles in three-dimensional gravity which provides an illuminating demonstration of what we hope to accomplish for full gravity. We develop the classical theory of point particles and show that it can be described by an evolving triangulation where discrete bistellar flips can occur. From here we define the loop gravity theory and show that it agrees with the continuous theory, having two-to-two moves on the graph which mirror the bistellar flips in the triangulation. The results are promising for finding a dynamics for four-dimensional loop gravity, and if the full theory is developed further, we expect it will lead to a breakthrough in the quantum dynamics.

Brown and York's gravitational microcanonical density of states is extended to general spacetime dimension and shown to be dependent upon features of the 4 dimensional gravitational action for its interpretation. Black hole entropy is calculated from the density of states path integral in general spacetime dimension, and the interpretation is shown to be likewise dependent upon the dimension of spacetime. The entropy of de Sitter and Rindler horizons are calculated using the black hole density of states and the notion of local horizon entropy density is shown to be supported. The applicability of the microcanonical ensemble to black hole mechanics is discussed at a fundamental level focussing on the absence of angular velocity as an external parameter in the gravitational Hamiltonian. The rotational ensemble and a new ensemble - the angular momentum ensemble - are introduced following Jaynes' information theory approach to statistical mechanics and proposed as more compelling candidates to calculate black hole entropy as a function of state. A program to calculate the density of states path integral non-perturbatively using causal dynamical triangulations is initiated. Regge calculus expressions for extrinsic curvature are extended to the case of Lorentzian hypersurfaces and used to derive Regge calculus expressions for quasilocal energy-momentum. The Regge version of the black hole density of states action is derived and specialised to the 3d and 4d spacetime constructions of causal dynamical triangulations. Finally, the recent suggestion that entropy is observer dependent is shown to be incompatible with the Tolman law for the equilibrium temperature in a gravitational field.

In this thesis we review the status of an approach to Quantum Gravity through lattice toy models, Quantum Graphity. In particular, we describe the two toy models introduced in the literature and describe with a certain level of details the results obtained so far. We emphasize the connection between Quantum Graphity and emergent gravity, and the relation with Variable Speed of Light theories.

Thesis (Ph. D.)--Montana State University--Bozeman, 2007. / Typescript. Chairperson, Graduate Committee: William A. Hiscock. Includes bibliographical references (leaves 55-60).

A thesis submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Doctor of Philosophy. 3rd October 2013. / A complete understanding of quantum gravity remains an open problem. However, the AdS/CFT correspondence which relates quantum eld theories that enjoy conformal symmetry to theories of (quantum) gravity is proving to be a useful tool in shedding light on this formidable problem. Recently developed group representation theoretic methods have proved useful in understanding the large N; but non-planar limit of N = 4 supersymmetric Yang-Mills theory. In this work, we study operators that are dual to excited giant gravitons, which corresponds to a sector of N = 4 super Yang-Mills theory that is described by a large N; but non-planar limit. After a brief review of the work done in the su (2) sector, we compute the spectrum of anomalous dimensions in the su (2) sector of the Leigh-Strassler deformed theory. The result resembles the spectrum of a shifted harmonic oscillator. We then explain how to construct restricted Schur polynomials built using both fermionic and bosonic elds which transform in the adjoint of the gauge group U (N) : We show that these operators diagonalise the free eld two point function to all orders in 1=N: As an application of our new operators, we study the action of the one-loop dilatation operator in the su (2,3) sector in a large N; but non-planar limit of N = 4 super Yang-Mills theory. As in the su (2) case, the resulting spectrum matches the spectrum of a set of decoupled oscillators. Finally, in an appendix, we study the action of the one-loop dilatation operator in an sl (2) sector of N = 4 super Yang-Mills theory. Again, the resulting spectrum matches that of a set of harmonic oscillators. In all these cases, we nd that the action of the dilatation operator is diagonalised by a double coset ansatz.

1In this dissertation we work out in detail a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, and propose how to compare in detail the physics of this sector with that of loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. To impose the symmetry at the quantum level, on both the connection and its conjugate momentum, the method used necessarily has similiarities to the Gupta-Bleuler method of quantizing the electromagnetic field. Lastly, a strategy for embedding states of loop quantum cosmology into this new homogeneous isotropic sector, and using this embedding to compare the physics, is presented. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

The spin-foam is a covariant path-integral style approaching to the quantization of the gravity. There exist several spin-foam models of which the most successful one is the Engle-Pereira-Rovelli-Levine/Freidel-Krasnov (EPRL-FK) model. Using the EPRLFK model people are able to calculate the transition amplitude and the n-point functions of 4D geometry (both Euclidean and Lorentzian) surrounding by a given triangulated 3D geometry. The semi-classical limit of the EPRL-FK amplitude reproduces discrete classical gravity under certain assumptions, which shows that the EPRLFK model can be understood as UV completion of general relativity. On the other hand, it is very hard to dene a continuum limit and couple a cosmological constant to the EPRL-FK model. In this dissertation, we addressed the problems about continuum limit and coupling a cosmological constant to the EPRL-FK model. Followed by chapter one as a brief introduction of the loop quantum gravity and EPRL-FK model, chapter two introduces our work about demonstrating (for the first time) that smooth curved spacetime geometries satisfying Einstein equation can emerge from discrete spin-foam models under an appropriate low energy limit, which corresponds to a semi-classical continuum limit of spin-foam models. In chapter three, we bring in the cosmological constant into the spin-foam model by coupling the SL(2, C) Chern-Simons action with the EPRL action, and find that the quantum simplicity constraint is realized as the 2d surface defect in SL(2, C)Chern-Simons theory in the construction of spin-foam amplitudes. In chapter four, we present a way to describe the twisted geometry with cosmological constant whose corresponding quantum states can forms the Hilbert space of the loop quantum gravity with cosmological constant. In chapter five, we introduced a new definition of the graviton propagator, and calculate its semi-classical limit in the contents of spin-foam model with the cosmological constant. Finally the chapter six will be a outlook for my future work. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection