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quantum spacetimes
This is a contributed topic on quantum spacetimes viewed from general relativistic and quantum gravity standpoints, and includes, for example, quantum geometry fundamental notions.
1 Quantum Spacetimes (QST)
The concept of quantum spacetimes (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 spacetimes or how to develop a valid classification theory of quantum spacetimes. 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 SpaceTimes (QSTs) and Quantum Geometry

QSTs represented by socalled quantum topoi (QTs) with Heyting logic algebra as a subobject classifier

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

QSTs represented as spin foams of spin networks

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

QSTs represented as generalized Riemannian manifolds with quantum tangent spaces

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

QSTs represented as consisting of quantum loops

QST represented as a quantum category of locally compact grpoupoids

QSTs represented as categories or spaces of quantized strings as in string theories

Twistor representations in quantum gravity (QG) (introduced by Sir Roger Penrose).
Mathematics Subject Classification
81R60 no label found81R50 no label found81P10 no label found83C47 no label found83C75 no label found83C45 no label found81P05 no label found Forums
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