quantum space-times
This is a contributed topic on quantum space-times 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 theories 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
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QSTs represented by posets or causal sets
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QSTs represented by so-called quantum topoi (QTs) with Heyting logic algebra as a subobject classifier
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QSTs represented by Topological Quantum Field Theories (TQFTs) or Homotopy QFTs
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QSTs represented as spin foams of spin networks (http://planetmath.org/SpinNetworksAndSpinFoams)
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QSTs represented as a noncommutative, algebraic– and/or “geometrical”–quantized space as in noncommutative geometry models for SUSY
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QSTs represented as generalized Riemannian manifolds with quantum tangent spaces
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QSTs represented as presheaves of local nets of quantum operators in Algebraic QFT
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QSTs represented as quantum fields (QF) on a (physical) lattice of geometric points
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QSTs represented as consisting of quantum loops
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QSTs represented as fractal dimension spaces
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QST represented as a quantum category of locally compact grpoupoids
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QSTs represented as categories or spaces of quantized strings as in string theories
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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 |