quantum space-times

This is a contributed topic on quantum space-timesPlanetmathPlanetmath viewed from general relativistic and quantum gravity standpoints, and includes, for example, quantum geometry fundamental notions.

1 Quantum Space-times (QST)

The concept of quantum space-times (QST) is fundamental to the development of relativistic quantum theoriesPlanetmathPlanetmath and at this point it can only be broadly defined as a class of mathematical spaces that allow the construction of quantum physical theories in a manner consistent with both relativistic principles and quantum gravity. There is no universal agreement amongst either theoretical physicists or mathematicians who work on Physical Mathematics about either a specific definition of such quantum space-times or how to develop a valid classification theory of quantum space-times. However, several specific definitions or models were proposed and a list of such examples is presented next.

1.1 Specific Definitions for Models of Quantum Space-Times (QSTs) and Quantum Geometry

  • QSTs represented by posets or causal sets

  • QSTs represented by so-called quantum topoi (QTs) with Heyting logic algebra as a subobject classifier

  • QSTs represented by Topological Quantum Field Theories (TQFTs) or HomotopyMathworldPlanetmathPlanetmath QFTs

  • QSTs represented as spin foams of spin networks (http://planetmath.org/SpinNetworksAndSpinFoams)

  • QSTs represented as a noncommutative, algebraic– and/or “geometrical”–quantized space as in noncommutative geometryPlanetmathPlanetmath models for SUSY

  • QSTs represented as generalized Riemannian manifolds with quantum tangent spacesMathworldPlanetmath

  • QSTs represented as presheaves of local nets of quantum operators in Algebraic QFT

  • QSTs represented as quantum fields (QF) on a (physical) lattice of geometric points

  • QSTs represented as consisting of quantum loops

  • QSTs represented as fractal dimension spaces

  • QST represented as a quantum categoryPlanetmathPlanetmathPlanetmath of locally compact grpoupoids

  • QSTs represented as categoriesMathworldPlanetmath or spaces of quantized strings as in string theories

  • Twistor representations in quantum gravity (QG) (introduced by Sir Roger Penrose).

Title quantum space-times
Canonical name QuantumSpacetimes
Date of creation 2013-03-22 18:15:56
Last modified on 2013-03-22 18:15:56
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 28
Author bci1 (20947)
Entry type Topic
Classification msc 81R60
Classification msc 81R50
Classification msc 81P10
Classification msc 83C47
Classification msc 83C75
Classification msc 83C45
Classification msc 81P05
Synonym QST
Synonym quantum state spaces
Synonym quantum spaces
Related topic QuantumFundamentalGroupoids
Related topic QuantumGroupoids2
Related topic QuantumGroups
Related topic QuantumSystem
Related topic QEDInTheoreticalAndMathematicalPhysics
Related topic HamiltonianOperatorOfAQuantumSystem
Related topic QuantumChromodynamicsQCD
Related topic QuantumAutomataAndQuantumComputation2
Related topic Quantization
Related topic QEDInTheoreticalAndMathema
Defines quantum space-time structure
Defines QST