7 research outputs found
Quantizing Horava-Lifshitz Gravity via Causal Dynamical Triangulations
We extend the discrete Regge action of causal dynamical triangulations to
include discrete versions of the curvature squared terms appearing in the
continuum action of (2+1)-dimensional projectable Horava-Lifshitz gravity.
Focusing on an ensemble of spacetimes whose spacelike hypersurfaces are
2-spheres, we employ Markov chain Monte Carlo simulations to study the path
integral defined by this extended discrete action. We demonstrate the existence
of known and novel macroscopic phases of spacetime geometry, and we present
preliminary evidence for the consistency of these phases with solutions to the
equations of motion of classical Horava-Lifshitz gravity. Apparently, the phase
diagram contains a phase transition between a time-dependent de Sitter-like
phase and a time-independent phase. We speculate that this phase transition may
be understood in terms of deconfinement of the global gravitational Hamiltonian
integrated over a spatial 2-sphere.Comment: 24 pages; 10 figure
Aspects of Black Hole Quantum Mechanics and Thermodynamics in 2+1 Dimensions
We discuss the quantum mechanics and thermodynamics of the (2+1)-dimensional
black hole, using both minisuperspace methods and exact results from
Chern-Simons theory. In particular, we evaluate the first quantum correction to
the black hole entropy. We show that the dynamical variables of the black hole
arise from the possibility of a deficit angle at the (Euclidean) horizon, and
briefly speculate as to how they may provide a basis for a statistical picture
of black hole thermodynamics.Comment: 20 pages and 2 figures, LaTeX, IASSNS-HEP-94/34 and UCD-94-1
Complete loop quantization of a dimension 1+2 Lorentzian gravity theory
De Sitter Chern-Simons gravity in D = 1 + 2 spacetime is known to possess an
extension with a Barbero-Immirzi like parameter. We find a partial gauge fixing
which leaves a compact residual gauge group, namely SU(2). The compacticity of
the residual gauge group opens the way to the usual LQG quantization
techniques. We recall the exemple of the LQG quantization of SU(2) CS theory
with cylindrical space topology, which thus provides a complete LQG of a
Lorentzian gravity model in 3-dimensional space-time.Comment: Loops11 - Madrid - 2011 (4 pages, Latex
Quantization of Lorentzian 3d Gravity by Partial Gauge Fixing
D = 2+1 gravity with a cosmological constant has been shown by Bonzom and
Livine to present a Barbero-Immirzi like ambiguity depending on a parameter. We
make use of this fact to show that, for positive cosmological constant, the
Lorentzian theory can be partially gauge fixed and reduced to an SU(2)
Chern-Simons theory. We then review the already known quantization of the
latter in the framework of Loop Quantization for the case of space being
topogically a cylinder. We finally construct, in the same setting, a quantum
observable which, although non-trivial at the quantum level, corresponds to a
null classical quantity.Comment: Notation defect fixed on pages 5 (bottom) and 6 (around Eqs. 3.1)--
19 pages, Late
The Nexus between Artificial Intelligence and Economics
This book is organized as follows. Section 2 introduces the notion of the Singularity, a stage in development in which technological progress and economic growth increase at a near-infinite rate. Section 3 describes what artificial intelligence is and how it has been applied. Section 4 considers artificial happiness and the likelihood that artificial intelligence might increase human happiness. Section 5 discusses some prominent related concepts and issues. Section 6 describes the use of artificial agents in economic modeling, and section 7 considers some ways in which economic analysis can offer some hints about what the advent of artificial intelligence might bring. Chapter 8 presents some thoughts about the current state of AI and its future prospects.