Exploring Causal Dynamical Triangulations

Download or read book Exploring Causal Dynamical Triangulations written by Joshua Harris Cooperman and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Causal dynamical triangulations is a novel approach to lattice regularization of the gravitational path integral. After motivating the study of quantum theories of gravity in general and of causal dynamical triangulations in particular in chapter 1, I introduce the theoretical formalism of causal dynamical triangulations in the context of quantizing Einstein gravity in chapter 2. I then explore a series of five topics in causal dynamical triangulations in the five ensuing chapters. I begin in chapter 3 by considering the gravitational effective action that describes the ensemble average quantum spacetime geometry on sufficiently large scales of (the ground state of a certain phase of) the causal dynamical triangulations of Einstein gravity. This discussion sets the stage for much of the analysis contained in the next four chapters. In chapter 4 I make substantial use of this effective action in developing a method for extracting renormalization group flows of gravitational couplings. Next I present in chapter 5 the spectral dimension, an observable measuring the scale dependent dimensionality of a space that has notably elucidated the physical nature of quantum spacetime geometry emerging from causal dynamical triangulations. Within the causal dynamical triangulations of (2+1)-dimensional Einstein gravity, I study transition amplitudes between past and future spacelike boundaries of fixed intrinsic geometries in chapter 6. Employing the techniques of causal dynamical triangulations, I perform a quantization of (2+1)-dimensional projectable Horava-Lifshitz gravity in chapter 7. Finally, I discuss my ongoing research in and the theoretical prospects for causal dynamical triangulations in chapter 8.