Quantum Spacetime: a Disambiguation

Abstract

We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular irreducible component is often referred to as the "canonical quantum spacetime". The aim is to distinguish and compare the approaches under various points of view, including motivations, prescriptions for quantisation, the choice of mathematical objects and concepts, approaches to dynamics and to covariance.

special issue of SIGMA "Noncommutative Spaces and Fields"

References in corpus (24)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Perturbative Dynamics
• A Generalized Uncertainty Principle in Quantum Gravity
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Space-Time Noncommutative Field Theories And Unitarity
• On the unitarity problem in space/time noncommutative theories
• Deformed Coordinate Spaces; Derivatives
• Time-ordered Perturbation Theory on Noncommutative Spacetime: Basic Rules
• Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
• Time-ordered Perturbation Theory on Noncommutative Spacetime II: Unitarity
• Field Theory on Noncommutative Spacetimes: Quasiplanar Wick Products
• Spacetime and Fields, a Quantum Texture
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators
• Time ordered perturbation theory for non-local interactions; applications to NCQFT
• Quantum Field Theory on Quantum Spacetime
• Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model
• Schwinger functions in noncommutative quantum field theory
• Lorentz Covariant k-Minkowski Spacetime
• Ultraviolet Finiteness of the averaged Hamiltonian on the noncommutative Minkowski space
• Non Local Theories: New Rules for Old Diagrams
• On the operator algebra for the space-time uncertainty relations
• Twisted Covariance and Weyl Quantisation
• Poincaré Covariant k-Minkowski Spacetime

Cited by in corpus (12)

• Physically motivated uncertainty relations at the Planck length for an emergent non commutative spacetime
• A fully covariant information-theoretic ultraviolet cutoff for scalar fields in expanding FRW spacetimes
• Beyond the Standard Model with noncommutative geometry, strolling towards quantum gravity
• Length and distance on a quantum space
• Propagators and Matrix Basis on Noncommutative Minkowski Space
• Poincaré Covariant k-Minkowski Spacetime
• A proposal for Heisenberg uncertainty principle and STUR for curved backgrounds: an application to white dwarf, neutron stars and black holes
• Covariant Fields of C*-Algebras under Rieffel Deformation
• Noncommutative geometry of the Moyal plane: translation isometries, Connes' distance on coherent states, Pythagoras equality
• Deformations of the Canonical Commutation Relations and Metric Structures
• The DFR-Algebra for Poisson Vector Bundles
• Wick rotation for quantum field theories on degenerate Moyal space(-time)