The Superspace of Geometrodynamics

Abstract

Wheeler's Superspace is the arena in which Geometrodynamics takes place. I review some aspects of its geometrical and topological structure that Wheeler urged us to take seriously in the context of canonical quantum gravity.

29 pages, 8 figures. To appear in the Wheeler memorial volume of General Relativity and Gravitation

References in corpus (20)

• Real Ashtekar Variables for Lorentzian Signature Space-times
• Real and complex connections for canonical gravity
• Relativity without relativity
• Canonical Quantum Gravity
• Is Barbero's Hamiltonian formulation a Gauge Theory of Lorentzian Gravity?
• What is the Geometry of Superspace ?
• Tunnelling Effect and Hawking Radiation from a Vaidya Black Hole
• Constraints and gauge transformations: Dirac's theorem is not always valid
• Wheeler-Dewitt Metric and the Attractivity of Gravity
• Symmetries,Singularities and the De-Emergence of Space
• A Spin-Statistics Theorem for Certain Topological Geons
• Constraints and the E10 Coset Model
• Properties of 3-manifolds for relativists
• Classical and Quantum Gravity on Conformal Superspace
• Generally covariant theories: the Noether obstruction for realizing certain space-time diffeomorphisms in phase space
• Orientation reversal of manifolds
• Quantum Mechanics On Spaces With Finite Fundamental Group
• An Analysis of the Representations of the Mapping Class Group of a Multi-Geon Three-Manifold
• On M-Theory
• Canonical Gravity, Diffeomorphisms and Objective Histories

Cited by in corpus (50)

• Homogeneous cosmologies as group field theory condensates
• Soft Gravitons & the Memory Effect for Plane Gravitational Waves
• Quantization of Midisuperspace Models
• Quantum cosmology of (loop) quantum gravity condensates: An example
• Observations in Quantum Cosmology
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• The Solution to the Problem of Time in Shape Dynamics
• The Smallest Shape Spaces. I. Shape Theory Posed, with Example of 3 Points on the Line
• Quantum Cosmology
• Coherent states for quantum gravity: towards collective variables
• Shape dynamics and Mach's principles: Gravity from conformal geometrodynamics
• Configuration Spaces in Fundamental Physics
• Discrete and continuum third quantization of Gravity
• A Definition of Background Independence
• Shape Theory. III. Comparative Theory of Backgound Independence
• Covariant singularities in Quantum Field Theory and Quantum Gravity
• A Local Resolution of the Problem of Time. II. Configurational Relationalism via a generalization of Group Averaging
• Gauge Theory in Riem(M)
• From path integrals to the Wheeler-DeWitt equation: Time evolution in spacetimes with a spatial boundary
• A Local Resolution of the Problem of Time. I. Introduction and Temporal Relationalism
• A Local Resolution of the Problem of Time. V. Combining Temporal and Configurational Relationalism for Finite Theories
• $N$-Body Problem: Minimal $N$'s for Qualitative Nontrivialities
• Shape Theories. II. Compactness Selection Principles
• Shape Theories. I. Their Diversity is Killing-Based and thus Nongeneric
• Problem of Time and Background Independence: classical version's higher Lie Theory
• A Local Resolution of the Problem of Time. XIV. Grounding on Lie's Mathematics
• Quantifying closeness between black hole spacetimes: a superspace approach
• A Note on the Topology of a Generic Subspace of Riem
• Problem of Time: Temporal Relationalism Compatibility of Other Local Classical Facets Completed
• On the proof of the Thin Sandwich Conjecture in arbitrary dimensions
• Solution of the noncanonicity puzzle in General Relativity: a new Hamiltonian formulation
• Background Independence: ${\mathbb{S}}^1$ and $\mathbb{R}$ absolute spaces differ greatly in Shape-and-Scale Theory
• Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity?
• Aspects of quantum gravity
• Rubber Relationalism: Smallest Graph-Theoretically Nontrivial Leibniz Spaces
• A metric on the space of neutron star models in general relativity and modified gravity
• The rotation problem
• On topology changes in quantum field theory and quantum gravity
• Local(ish) gravity theories in conformal superspace
• Quantum Reference Frames via Transition Amplitudes in Timeless Quantum Gravity
• Geometric distances between closed universes
• Quantum Cosmology
• Space, Time, Matter in Quantum Gravity
• On the Geometric Quantization of Canonical Gravity
• Two problems in the theory of differential equations
• Arkady Onishchik: on his life and work on supersymmetry
• An approximate application of quantum gravity to the rotation problem
• The Space of Connections as the Arena for (Quantum) Gravity
• The Canonical Lagrangian Approach To Three-Space General Relativity
• Isotropy Groups and Kinematic Orbits for 1 and 2-$d$ $N$-Body Problems