A perturbative approach to Dirac observables and their space-time algebra
arXiv:gr-qc/0610060 · doi:10.1088/0264-9381/24/4/001
Abstract
We introduce a general approximation scheme in order to calculate gauge invariant observables in the canonical formulation of general relativity. Using this scheme we will show how the observables and the dynamics of field theories on a fixed background or equivalently the observables of the linearized theory can be understood as an approximation to the observables in full general relativity. Gauge invariant corrections can be calculated up to an arbitrary high order and we will explicitly calculate the first non--trivial correction. Furthermore we will make a first investigation into the Poisson algebra between observables corresponding to fields at different space--time points and consider the locality properties of the observables.
23 pages
References in corpus (1)
Cited by in corpus (56)
- Loop Quantum Cosmology: A Status Report
- The Spin Foam Approach to Quantum Gravity
- The Trinity of Relational Quantum Dynamics
- Diffeomorphism-invariant observables and their nonlocal algebra
- Anomaly freedom in perturbative loop quantum gravity
- An effective approach to the problem of time
- Effective approach to the problem of time: general features and examples
- Relational Observables in Gravity: a Review
- Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity
- Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?
- Switching internal times and a new perspective on the 'wave function of the universe'
- Loop quantum gravity: the first twenty five years
- Anomaly-free cosmological perturbations in effective canonical quantum gravity
- Manifestly Gauge-Invariant General Relativistic Perturbation Theory: I. Foundations
- Equivalence of approaches to relational quantum dynamics in relativistic settings
- Cosmological vector modes and quantum gravity effects
- Linearized dynamics from the 4-simplex Regge action
- From covariant to canonical formulations of discrete gravity
- Beables/Observables in Classical and Quantum Gravity
- Effective relational dynamics of a nonintegrable cosmological model
- How to switch between relational quantum clocks
- Time evolution as refining, coarse graining and entangling
- Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order
- Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
- Can chaos be observed in quantum gravity?
- On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity
- Towards a reduced phase space quantization in loop quantum cosmology with an inflationary potential
- Gauge invariant variables for cosmological perturbation theory using geometrical clocks
- Quantum fields, non-locality and quantum group symmetries
- Observations in Quantum Cosmology
- Mukhanov-Sasaki equation in manifestly gauge-invariant linearized cosmological perturbation theory with dust reference fields
- Towards effective actions for the continuum limit of spin foams
- Quantum Null Geometry and Gravity
- LTB spacetimes in terms of Dirac observables
- A Note on B-observables in Ponzano-Regge 3d Quantum Gravity
- Solving the Problem of Time in Mini-superspace: Measurement of Dirac Observables
- Quantum astrometric observables I: time delay in classical and quantum gravity
- Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory
- The Montevideo Interpretation: How the inclusion of a Quantum Gravitational Notion of Time Solves the Measurement Problem
- A gravitationally induced decoherence model using Ashtekar variables
- Chaos, Dirac observables and constraint quantization
- On consistent gauge fixing conditions in polymerized gravitational systems
- Quantum astrometric observables II: time delay in linearized quantum gravity
- Born--Oppenheimer decomposition for quantum fields on quantum spacetimes
- Quantum gravity in timeless configuration space
- Synchronous coordinates and gauge-invariant observables in cosmological spacetimes
- Restoration of four-dimensional diffeomorphism covariance in canonical general relativity: An intrinsic Hamilton-Jacobi approach
- Perspective-neutral approach to quantum frame covariance for general symmetry groups
- Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
- Gravitationally induced decoherence of a scalar field: investigating the one-particle sector and its interplay with renormalisation
- A Momentous Arrow of Time
- Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
- Relational Dynamics with Periodic Clocks
- Barnich-Troessaert Bracket as a Dirac Bracket on the Covariant Phase Space
- Loop quantum gravity - a short review
- Diffeomorphism-Invariant Quantities in Phase Space: More than Correlations