Spacetime and Fields, a Quantum Texture

Abstract

We report on joint work, past and in progress, with K.Fredenhagen and with J.E,Roberts, on the quantum structure of spacetime in the small which is dictated by the principles of Quantum Mechanics and of General Relativity; we comment on how these principles point to a deep link between coordinates and fields. This is an expanded version of a lecture delivered at the 37th Karpacz School in Theoretical Physics, February 2001.

LaTeX, 15 pages. Misprints and wording corrected, references added; change in section 3. Related references: hep-th/0303037, hep-th/0201222, hep-th/0301100

References in corpus (3)

• The quantum structure of spacetime at the Planck scale and quantum fields
• On the unitarity problem in space/time noncommutative theories
• Noncommutative Parameters of Quantum Symmetries and Star Products

Cited by in corpus (30)

• Noncommutative Field Theory
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Noncommutative Gravity Solutions
• Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
• Noncommutative field theory with the Wick-Voros product
• Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators
• On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes
• Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies
• On Quantum Spacetime and the horizon problem
• Quantum Spacetime: a Disambiguation
• Quantum Field Theory on Quantum Spacetime
• Quasinormal Modes in Noncommutative Schwarzschild black holes
• Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere
• Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model
• Modular Theory, Non-Commutative Geometry and Quantum Gravity
• The Gribov problem in Noncommutative QED
• Entropy, energy and temperature-length inequality for Friedmann universes
• Planckian corrections to the Friedmann flat equations from thermodynamics at the apparent horizon
• Length and distance on a quantum space
• Comment on "Can we measure structures to a precision better than the Planck length?"[arXiv:1205.3636], by Sabine Hossenfelder
• The cosmological constant from Planckian fluctuations and the averaging procedure
• Spin and Statistics and First Principles
• The Fuzzy Analog of Chiral Diffeomorphisms in higher dimensional Quantum Field Theories
• Space-time noncommutativity and (1+1) Higgs Model
• On the distance observable in the Moyal plane and in a novel two-dimensional space with string-theory pregeometry
• The Structure of Spacetime and Noncommutative Geometry
• Renormalization on the DFR Quantum Spacetime
• Einstein's lifts and topologies: topological investigations on the Principle of Equivalence
• On 2d gravity and parallel transport field equation on quantum sphere
• The 3D perturbed Schrödinger Hamiltonian in a Friedmann flat spacetime testing the primordial universe in a non commutative spacetime