The Small Scale Structure of Space-Time: A Bibliographical Review

Abstract

This essay is a tour around many of the lesser known pregeometric models of physics, as well as the mainstream approaches to quantum gravity, in search of common themes which may provide a glimpse of the final theory which must lie behind them.

50 pages, TeX (two references added)

References in corpus (54)

• The World as a Hologram
• Discreteness of area and volume in quantum gravity
• A Generalized Uncertainty Principle in Quantum Gravity
• Introduction to string field theory
• Closed String Field Theory: Quantum Action and the BV Master Equation
• Weaving a classical geometry with quantum threads
• Topological Lattice Models in Four Dimensions
• On Background Independent Open-String Field Theory
• A Model of Three-Dimensional Lattice Gravity
• Production of Kaluza-Klein States at Future Colliders
• Entropy Bounds and Black Hole Remnants
• Dirac and Weyl Equations on a Lattice as Quantum Cellular Automata
• Strings, Black Holes and Lorentz Contraction
• The basis of the Ponzano-Regge-Turaev-Viro-Ooguri model is the loop representation basis
• An Equivalence Between Momentum and Charge in String Theory
• Critical Behavior of Dynamically Triangulated Quantum Gravity in Four Dimensions
• Discrete differential calculus, graphs, topologies and gauge theory
• Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity
• Partition Functions and Topology-Changing Amplitudes in the 3D Lattice Gravity of Ponzano and Regge
• Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes
• String Bit Models for Superstring
• Introduction to Braided Geometry and $q$-Minkowski Space
• Differential calculus and gauge theory on finite sets
• Structure of Topological Lattice Field Theories in Three Dimensions
• An introduction to quantized Lie groups and algebras
• NON-PERTURBATIVE SOLUTIONS FOR LATTICE QUANTUM GRAVITY
• Quantum Mechanics, Common Sense and the Black Hole Information Paradox
• A definition of the Ponzano-Regge quantum gravity model in terms of surfaces
• The Lagrangian of q-Poincare' Gravity
• Quantum Group Gauge Theories and Covariant Quantum Algebras
• On the Absence of an Exponential Bound in Four Dimensional Simplicial Gravity
• Fractional Superstrings with Space-Time Critical Dimensions Four and Six
• Topological Field Theory As The Key To Quantum Gravity
• Calculating the Rest Tension for a Polymer of String Bits
• Discrete Time from Quantum Physics
• Field Theory of Open and Closed Strings with Discrete Target Space
• A Step Toward Pregeometry I.: Ponzano-Regge Spin Networks and the Origin of Spacetime Structure in Four Dimensions
• General compact quantum groups, a tutorial
• The Propagators of Gauge Bosons on a lattice
• Finite Approximations to Quantum Physics: Quantum Points and their Bundles
• Discrete Strings and Deterministic Cellular Strings
• Manifestations of Space-Time Multidimensionality in Scattering of Scalar Particles
• Quantum gravity, the Planck lattice and the Standard Model
• Event-Symmetric Physics
• Symmetry in the Topological Phase of String Theory
• Surgical invariants of four-manifolds
• A Hierarchy of Super $w$\ Strings
• ``Theory of Theories'' Approach to String Theory
• MATRIX MODELS FOR SPACETIME TOPODYNAMICS
• Towards a Canonical Formalism of Field Theory on Discrete Spacetime
• Bound on nonlocal scale from LEP
• A symplectic structure for the space of quantum field theories
• Weyl Neutrinos on a Lattice: An Explicit Construction
• The Langevin equation on a cell complex

Cited by in corpus (22)

• Emergent Hyperbolic Network Geometry
• Structural Issues in Quantum Gravity
• Localization of Events in Space-Time
• Umbral Calculus, Difference Equations and the Discrete Schroedinger Equation
• Statistical Lorentzian geometry and the closeness of Lorentzian manifolds
• Glimmers of a pre-geometric perspective
• Emergence of the Circle in a Statistical Model of Random Cubic Graphs
• Noncommutative Kaluza-Klein Theory
• Bootstrap Universe from Self-Referential Noise
• Pregeometric modelling of the spacetime phenomenology
• Emergence of Space-Time on the Planck Scale described as an Unfolding Phase Transition within the Scheme of Dynamical Cellular Networks and Random Graphs
• Non-linear quantum mechanics and high energy cosmic rays
• In Search of Local Degrees of Freedom in Quadratic Diff-invariant Lagrangians
• Dynamical Evolution in Noncommutative Discrete Phase Space and the Derivation of Classical Kinetic Equations
• Beneath Gauge
• Does matter differ from vacuum?
• Mathematical Structure of Discrete Space-time
• A metageometric enquiry concerning time, space, and quantum physics
• Reality - an emerging representation of the world
• Unified meta-theory of information, consciousness, time and the classical-quantum universe
• Semiclassical Length Measure from a Quantum-Gravity Wave Function
• On Dynamical Quantization