PlanetPhysics/Theoretical Programs in Quantum Gravity

There are several distinct research [[../SupercomputerArchitercture/|programs]] aimed at developing the mathematical foundations of [[../SpaceTimeQuantizationInQuantumGravityTheories/|quantum gravity theories]]. These include, but are not limited to, the following.

Mathematical Programs being Developed in Quantum Gravity

1. The twistors program applied to an open curved [[../SR/|space-time]] (see refs.

), (which is presumably a globally hyperbolic, relativistic space-time). This may also include the idea of developing a `sheaf cohomology' for twistors (see ref. ) but still needs to justify the assumption in this approach of a charged, fundamental [[../Fermion/|fermion]] of spin-3/2 of undefined [[../CosmologicalConstant/|mass]] and unitary `homogeneity' (which has not been observed so far);

1. The [[../AntiCommutationRelations/|supergravity]] theory program, which is consistent with [[../AntiCommutationRelations/|supersymmetry]] and [[../NewtonianMechanics/|superalgebra]], and utilizes graded [[../BilinearMap/|Lie algebras]] and \emph{matter-coupled

[[../AntiCommutationRelations/|superfields]]} in the presence of weak gravitational [[../CosmologicalConstant2/|fields]];

1. The no [[../GenericityInOpenSystems/|boundary]] (closed), continuous space-time programme (ref.

) in quantum cosmology, concerned with singularities, such as black and `white' holes; S. W. Hawking combines, joins, or glues an initially flat Euclidean [[../MetricTensor/|metric]] with convex [[../LebesgueMeasure/|Lorentzian]] metrics in the expanding, and then contracting, space-times with a very small value of [[../AlbertEinstein/|Einstein's]] [[../CosmologicalConstant/|cosmological `constant]]'. Such Hawking, double-pear shaped, space-times also have an initial Weyl [[../Tensor/|tensor]] value close to zero and, ultimately, a largely fluctuating Weyl tensor during the `final crunch' of our [[../MultiVerses/|Universe]], presumed to determine the irreversible arrow of time; furthermore, an observer will always be able to access through measurements only a limited part of the global space-times in our universe;

1. The [[../SUSY2/|TQFT/]] approach that aims at finding the [[../ModuleAlgebraic/|topological invariants]] of a

[[../NoncommutativeGeometry4/|manifold]] embedded in an abstract [[../VectorSpace2/|vector space]] related to the [[../ThermodynamicLaws/|statistical mechanics]] problem of defining extensions of the partition [[../Bijective/|function]] for many-particle quantum [[../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]];

1. The string and [[../10DBrane/|superstring]] theories/M-theory that `live' in higher dimensional

spaces (e.g., $n\ge 6$, preferred $n-dim=11$), and can be considered to be [[../CoIntersections/|topological]] [[../CategoricalGroupRepresentation/|representations]] of physical entities that vibrate, are quantized, interact, and that might also be able to predict fundamental masses relevant to [[../QuantumParticle/|quantum particles]];

1. The `[[../Categorification3/|categorification]]' and [[../Cod/|groupoidification]] programs () that aims to deal with [[../CosmologicalConstant/|quantum field]] and [[../SUSY2/|QG]] problems at the abstract level of [[../Cod/|categories]] and [[../Functor/|functors]] in what seems to be mostly a global approach;
2. The `monoidal category' and valuation approach initiated by Isham to the [[../CosmologicalConstant/|quantum measurement]] problem and its possible solution through local-to-global, finite constructions in [[../SmallCategory/|small categories]].