quantum space-times
This is a fundamental topic on quantum space-times viewed from general relativistic and quantum gravity
(QG) standpoints, and includes, for example, quantum geometry
fundamental notions.
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.
- QSTs represented by posets or causal sets
- QSTs represented by so-called quantum topoi with Heyting logic algebra as 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 (AQFT)
- QSTs represented as Quantum Fields on a (physical) Lattice of geometric points
- QSTs represented as consisting of quantum loops
- QSTs represented as fractal dimension spaces
- QSTs represented as categories or spaces of quantized strings as in string theories
- Twistor representations in Quantum Gravity (QG) (introduced by Sir Roger Penrose).
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As of this snapshot date, this entry was owned by bci1.