Non-commutative coordinates from quantum gravity
arXiv:2303.17238 · doi:10.22323/1.436.0307
Abstract
Local observables in (perturbative) quantum gravity are notoriously hard to define, since the gauge symmetry of gravity -- diffeomorphisms -- moves points on the manifold. In particular, this is a problem for backgrounds of high symmetry such as Minkowski space or de Sitter spacetime which describes the early inflationary phase of our universe. Only recently this obstacle has been overcome, and a field-dependent coordinate system has been constructed to all orders in perturbation theory, in which observables are fully gauge-invariant. We show that these field-dependent coordinates are non-commutative, and compute their commutator to second order in the Planck length. This provides the first systematic derivation of non-commutativity that arises due to quantum gravity effects.
arXiv commentProceedings of the Corfu Summer Institute 2022 "School and Workshops on Elementary Particle Physics and Gravity". Based on arXiv:2207.03345 [gr-qc]. 12 pages
References in corpus (30)
- Noncommutative Field Theory
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- The quantum structure of spacetime at the Planck scale and quantum fields
- A Generalized Uncertainty Principle in Quantum Gravity
- Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
- Noncommutative geometry inspired Schwarzschild black hole
- Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
- Quantum Groups, Gravity, and the Generalized Uncertainty Principle
- On Gravity and the Uncertainty Principle
- Generalized Uncertainty Principle: Approaches and Applications
- Emergent Geometry and Gravity from Matrix Models: an Introduction
- Generalized Uncertainty Principle, Extra-dimensions and Holography
- GUP parameter from quantum corrections to the Newtonian potential
- Quantum Measurement, Gravitation, and Locality
- Uncertainty Relation on World Crystal and its Applications to Micro Black Holes
- Light-cone averaging in cosmology: formalism and applications
- Relational Observables in Gravity: a Review
- Horizon wave-function for single localized particles: GUP and quantum black hole decay
- The century of the incomplete revolution: searching for general relativistic quantum field theory
- Local covariant quantum field theory over spectral geometries
- A noncommutative view on topology and order
- The -(A)dS noncommutative spacetime
- Mukhanov-Sasaki equation in manifestly gauge-invariant linearized cosmological perturbation theory with dust reference fields
- Temporal Lorentzian Spectral Triples
- Non-commutative Geometry from Perturbative Quantum Gravity
- Cosmological Perturbations and Invariant Observables in Geodesic Lightcone Coordinates
- The Cosmological Perturbation Theory on the Geodesic Light-Cone background
- Light-cone coordinates based at a geodesic world line
- Natural vs. Artificial Topologies on a Relativistic Spacetime
- On Global Hyperbolicity of Spacetimes: Topology Meets Functional Analysis