Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)

Abstract

These are lecture notes on causal set theory prepared in Jan. 2002 for a Summer School in Valdivia, Chile. In some places, they are more complete, in others much less so, regrettably. An extensive set of references and a glossary of terms can be found at the end of the notes.

plainTeX, 27 pages, no figures To appear in the proceedings of the Valdivia Summer School, edited by A. Gomberoff and D. Marolf

References in corpus (7)

• Evidence for a continuum limit in causal set dynamics
• On the "renormalization" transformations induced by cycles of expansion and contraction in causal set cosmology
• Statistical Lorentzian geometry and the closeness of Lorentzian manifolds
• General Covariance and the "Problem of Time" in a Discrete Cosmology
• The fate of black hole singularities and the parameters of the standard models of particle physics and cosmology
• Moment Problems and the Causal Set Approach to Quantum Gravity
• Causal Sets, a Possible Interpretation for the Black Hole Entropy,and Related Topics

Cited by in corpus (92)

• Analogue Gravity
• Spectral Dimension of the Universe
• A Topos Foundation for Theories of Physics: I. Formal Languages for Physics
• The birth of spacetime atoms as the passage of time
• Causal categories: relativistically interacting processes
• The Geometry of Small Causal Diamonds
• Scalar Field Theory on a Causal Set in Histories Form
• Evidence for a Phase Transition in 2D Causal Set Quantum Gravity
• A closed form expression for the causal set d'Alembertian
• Directions in Causal Set Quantum Gravity
• The Random Walk in Generalized Quantum Theory
• The Attractor and the Quantum States
• Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory
• Entanglement Entropy in Causal Set Theory
• A noncommutative view on topology and order
• A Lorentzian Gromov-Hausdoff notion of distance
• Does quantum mechanics tell an atomistic spacetime?
• Background independent condensed matter models for quantum gravity
• The moduli space of isometry classes of globally hyperbolic spacetimes
• Evolution of Universes in Causal Set Cosmology
• Experimental Search for Quantum Gravity
• Light, Links and Causal Sets
• On the Causal Set-Continuum Correspondence
• On the Axioms of Causal Set Theory
• Note on the existence theorem in ``Emergent Quantum Mechanics and Emergent Symmetries''
• Properties of Quantum Graphity at Low Temperature
• The Geometry of Large Causal Diamonds and the No Hair Property of Asymptotically de-Sitter Spacetimes
• Lorentzian Manifolds and Causal Sets as Partially Ordered Measure Spaces
• Causality and statistics on the Groenewold-Moyal plane
• Unambiguous Quantum Gravity Phenomenology Respecting Lorentz Symmetry
• Big extra dimensions make Lambda too small
• Causal sets and the deep structure of spacetime
• Visions in Quantum Gravity
• A covariant causal set approach to discrete quantum gravity
• Particle simulations in causal set theory
• Causal Set Generator and Action Computer
• Distinguishing Causality Principles
• Towards Spectral Geometry for Causal Sets
• Being, Becoming and the Undivided Universe: A Dialogue between Relational Blockworld and the Implicate Order Concerning the Unification of Relativity and Quantum Theory
• Challenges for Emergent Gravity
• Insights on Entanglement Entropy in $1+1$ Dimensional Causal Sets
• Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity
• Appearing Out of Nowhere: The Emergence of Spacetime in Quantum Gravity
• Notes on the Causal Structure in a Tensor Network
• `Iconoclastic', Categorical Quantum Gravity
• Popescu-Rohrlich Boxes in Quantum Measure Theory
• The Geometry of Small Causal Cones
• A discrete nonetheless remarkable brick in de Sitter: the "massless minimally coupled field"
• Discrete spacetime and its applications
• Discrete mechanics: a sequential growth dynamics for causal sets, and a self-organization of particles
• Spacetime and Matter - a duality of partial orders
• An Einstein equation for discrete quantum gravity
• A quantum field theory as emergent description of constrained supersymmetric classical dynamics
• Discrete mechanics: a kinematics for a particular case of causal sets
• Two-spinor geometry and gauge freedom
• Recovering General Relativity from a Planck scale discrete theory of quantum gravity
• Curvature and Quantum Mechanics on Covariant Causal Sets
• An Approach to Discrete Quantum Gravity
• The use of test functions to help define quadratic Lagrangian on a causal set
• Restoring locality of scalar fields on a causal set by avoiding the use of d'Alembertians
• Unfaithful embedding of causal sets
• A Matter of Matter and Antimatter
• Discrete mechanics: a sequential growth dynamics for causal sets that is based on binary alternatives
• Simple indicators for Lorentzian causets
• Causal Set Phenomenology
• A sequential growth dynamics for a directed acyclic dyadic graph
• Analysis of disk scheduling, increasing subsequences and space-time geometry
• A Unified Approach to Discrete Quantum Gravity
• The Causal Poset is Directed but not Lattice Ordered
• Constraints on Chronologies
• Gauge Invariance from a Graphical Self-Consistency Criterion
• Ph.D. Thesis: Quantum Field Theory and Gravity in Causal Sets
• Gravitation and cosmology with York time
• On the recovery of geometrodynamics from two different sets of first principles
• Emergence of Four Dimensions in the Causal Set Approach to Discrete Quantum Gravity
• Causal spin foams and the ontology of spacetime
• An Adynamical, Graphical Approach to Quantum Gravity and Unification
• Causal Set Topology
• The Relativistic Transactional Interpretation and Spacetime Emergence
• The Formation of the Universe: Conjectures
• Inter-theory Relations in Quantum Gravity: Correspondence, Reduction, and Emergence
• Unweaving the Fabric of the Universe: The Interplay between Mathematics and Physics
• Causal set approach to discrete quantum gravity
• Wave Equations for Discrete Quantum Gravity
• In search of relativistic time
• Elementary Particles and the Causet Approach to Discrete Quantum Gravity
• Discrete Quantum Gravity Is Not Isometric
• Labeled Causets in Discrete Quantum Gravity
• Spontaneous decoherence as a result of randomness in the flow of time
• The dynamics of binary alternatives for a discrete pregeometry
• General Formulation of Topos Many-Node Theory
• The Transactional Interpretation and its Evolution into the 21st Century: An Overview