Spectrum of the Volume Operator in Quantum Gravity
arXiv:gr-qc/9511030 · doi:10.1016/0550-3213(95)00627-3
Abstract
The volume operator is an important kinematical quantity in the non-perturbative approach to four-dimensional quantum gravity in the connection formulation. We give a general algorithm for computing its spectrum when acting on four-valent spin network states, evaluate some of the eigenvalue formulae explicitly, and discuss the role played by the Mandelstam constraints.
14 pages, plain tex, 4 figures (postscript, compressed and uu-encoded)
References in corpus (1)
Cited by in corpus (57)
- Background Independent Quantum Gravity: A Status Report
- Loop Quantum Gravity
- Quantum Gravity: a Progress Report
- Spin Foam Models
- The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
- Discrete approaches to quantum gravity in four dimensions
- Gauge Field Theory Coherent States (GCS) : I. General Properties
- Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
- Geometry Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity
- The Immirzi parameter in quantum general relativity
- The Area Operator in the Spherically Symmetric Sector of Loop Quantum Gravity
- Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections
- Closed formula for the matrix elements of the volume operator in canonical quantum gravity
- Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
- Gauge Field Theory Coherent States (GCS) : IV. Infinite Tensor Product and Thermodynamical Limit
- Quantum Theory of Geometry III: Non-commutativity of Riemannian Structures
- SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameter
- Quantum Spin Dynamics (QSD) : VII. Symplectic Structures and Continuum Lattice Formulations of Gauge Field Theories
- The length operator in Loop Quantum Gravity
- Quantum geometry with intrinsic local causality
- Area spectrum in Lorentz covariant loop gravity
- Properties of the Volume Operator in Loop Quantum Gravity I: Results
- Supersymmetric Spin Networks and Quantum Supergravity
- Matrix Elements of Thiemann's Hamiltonian Constraint in Loop Quantum Gravity
- Discrete Space-Time Volume for 3-Dimensional BF Theory and Quantum Gravity
- Loop Quantum Gravity
- Physical Properties of Quantum Field Theory Measures
- Simplifying the spectral analysis of the volume operator
- Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
- Eleven dimensional supergravity as a constrained topological field theory
- General geometric operators in all dimensional loop quantum gravity
- A real alternative to quantum gravity in loop space
- The spectrum of quantum black holes and quasinormal modes
- Coherent States for Black Holes
- Towards Loop Quantization of Plane Gravitational Waves
- Modelling Space with an Atom of Quantum Geometry
- Further results on geometric operators in quantum gravity
- A candidate for a background independent formulation of M theory
- Quantum states of elementary three-geometry
- Isotropic Loop Quantum Cosmology with Matter II: The Lorentzian Constraint
- Long range correlations in quantum gravity
- Imposing det E > 0 in discrete quantum gravity
- On Loop States in Loop Quantum Gravity
- Strings as perturbations of evolving spin-networks
- Quasilocal Energy for Spin-net Gravity
- Entropy and Area of Black Holes in Loop Quantum Gravity
- The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator
- Latticing quantum gravity
- The fermionic contribution to the spectrum of the area operator in nonperturbative quantum gravity
- Towards a background independent approach to M theory
- Classical and Quantum Polyhedra
- Embedded graph invariants in Chern-Simons theory
- Fermion mass gap in the loop representation of quantum gravity
- Properties of the Rovelli-Smolin-DePietri volume operator in the spaces of monochromatic intertwiners
- Entropy and Area in Loop Quantum Gravity
- Quantum volume and length fluctuations in a midi-superspace model of Minkowski space
- Categorical Quantum Volume Operator