In Search of Fundamental Discreteness in 2+1 Dimensional Quantum Gravity
arXiv:0906.3547 · doi:10.1088/0264-9381/26/18/185011
Abstract
Inspired by previous work in 2+1 dimensional quantum gravity, which found evidence for a discretization of time in the quantum theory, we reexamine the issue for the case of pure Lorentzian gravity with vanishing cosmological constant and spatially compact universes of genus larger than 1. Taking as our starting point the Chern-Simons formulation with Poincare gauge group, we identify a set of length variables corresponding to space- and timelike distances along geodesics in three-dimensional Minkowski space. These are Dirac observables, that is, functions on the reduced phase space, whose quantization is essentially unique. For both space- and timelike distance operators, the spectrum is continuous and not bounded away from zero.
29 pages, 18 figures
References in corpus (29)
- Quantum gravity and minimum length
- Quantum Gravity: a Progress Report
- Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
- Partial and Complete Observables for Canonical General Relativity
- Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
- The Nonperturbative Quantum de Sitter Universe
- Symplectic structure of the moduli space of flat connections on a Riemann surface
- Gravitational Observables and Local Symmetries
- The basis of the Ponzano-Regge-Turaev-Viro-Ooguri model is the loop representation basis
- Reduced Phase Space Quantization and Dirac Observables
- Structural Issues in Quantum Gravity
- Tangent Lifts of Poisson and Related Structures
- Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?
- Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity
- Revisiting observables in generally covariant theories in the light of gauge fixing methods
- Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity
- 4-Dimensional BF Theory as a Topological Quantum Field Theory
- Canonical Quantization of Gravitating Point Particles in 2+1 Dimensions
- Quantum Gravity in 2+1 Dimensions
- A Minimal Length from the Cutoff Modes in Asymptotically Safe Quantum Gravity
- Properties of the Volume Operator in Loop Quantum Gravity I: Results
- Cosmological Time in (2+1) - Gravity
- A locally finite model for gravity
- Cosmological measurements, time and observables in (2+1)-dimensional gravity
- Covariant Lattice Theory and t'Hooft's Formulation
- QUANTUM ASPECTS OF 2+1 GRAVITY
- Grafting and Poisson structure in (2+1)-gravity with vanishing cosmological constant
- The polygon model for 2+1D gravity: the constraint algebra and problems of quantization
- Linear structures on measured geodesic laminations